Looking at the Lists of fetters I see "conceit" and "identity view" listed separately ... and the four stages of enlightenment say that identity view will be abandoned (in the first stage) before conceit (in the fourth stage).
Wikipedia article about Conceit includes,
There is conceit or pride when we consider ourselves important.
How is it that "conceit" could continue after "identity view" has been abandoned?
A view is taking something to be true, whereas conceit falls in the category of a simple experience, which one may or may not hold to be valid. It is similar with greed; one may want something without believing it proper to want, and one may likewise feel conceit ("I am better", etc.) without actually believing in a self. This is seen when, after the arising of a conceited thought, one mentally discards it as being based on delusion rather than accepting it as valid.
Identity view, sakkāya-diṭṭhi, is the belief that the aggregates are self; it is this belief that gives rise to conceit, greed, anger, etc., but it is seperate from all of these. It is useful to remember that, while one without sakkāya-diṭṭhi can still give rise to defilement, such defilements are only remnants of past belief in self and are certain to disappear within seven lifetimes at most.
Mahasi Sayadaw discusses the difference and as always has interesting things to say:
At the stage of Sotāpanna, Stream Enterer, the fetters of Personality-belief (false view of individuality), doubts and uncertainty, and adherence to rites and rituals have been completely eradicated. But a Stream Enterer is not yet free from Asmi-māna, the I-conceit. To take pride in one's ability, one's status, "I can do; I am noble," is to hold on to the I-conceit. But a Stream Winner's conceit relates only to the genuine qualities and virtues, he actually possesses and is not false pride based on non-existing qualities and virtues.
What he is referring to is that fact that of the nine types of conceit, only three can arise in a sotapanna. The factors are:
and
(3x3=9)
and a Sotapanna can only give rise to true conceit, viz:
Mahasi Sayadaw also discusses the curious case of Khemaka, who was struggling with the difference himself (asmi means "I am", māna is conceit):
Asmi māna was once the subject of discussion between the sixty elder monks and Ashin Khemaka, an Anāgāmi, on the question of Arahatship. The latter told them through their intermediary, Dasaka, that he could not discover atta-self, or its attributes in any of the upādānakkhandhās, aggregates of clinging. The elders then concluded that he had become an Arahat and asked him if he was. This called for further elucidation and so he said, "I cannot as yet own myself an Arahat, but I have the notion that I am still in the realm of the five aggregates of clinging (asmīti adhigatam), although I would hesitate to say that this particular thing is 'I'. Then the elders again enquired, "Does I exist in feeling, or perception, or mental formations or consciousness?"
This drove Ashin Khemaka to the presence of the elders so that he could offer a personal explanation which runs as follows-
"Brothers! I cannot say I am matter; nor can I say I am feeling or perception or mental formation: or consciousness or any other beyond the five aggregates. But there still clings to me the notion that I am still in the realm of the five aggregates. But at the same time I cannot say, "This is I."
Ashin Khemaka did not consider any one of the upādānakkhandhās as asmī in the conventional sense. This term suggests that he thought, "I know. I can. I am great." This is self-conceit which grows out of the accomplishment of virtue that he had truly achieved. Consider the fragrance of a water-lily. Does it originate from its stem? From its petals? From its anothers? One can say only conventionally that it emanates from the lily, but one cannot find any rūpa matter that produces fragrance. The notion of asmī is there; but I cannot say, "This is I".
Ashin Khemaka then continued, "An Ariya (the Noble One) destroys the bonds of individuality, doubts, false religious practices, lust and animosity. But at this stage he cannot break away from asmī māna, asmī chanda and anusaya māna. They are subtle kinds of attachment to self, desire for self and inclination toward self. If, however the Ariyan disciple notes with mindfulness the arising and passing away of the five aggregates of clinging, such subtle passions will subside.
"Consider this metaphor of a washerwoman. She washes clothes with soap and water and they become clean-white. Still they smell of soap. Only when they are kept in a scented box they lose their odour. If one continually meditates on the five aggregates of clinging, all these subtle passions will be washed away clean and one can remain without any vestiges of such passions.
Identity view is a view or belief that there is an entity that exist within one the five khandas, is one of the five khandas, apart from the five khandas, contains one, or more, or all of the five khandas.
When it is discerned that there isn't an entity called a "self", that it doesn't exist, that it is a made up, mistaken view, held strongly, and there are only the five khandas and the workings of Dependent Origination, there still exist the view of "I am" as a reference point.
Where there still exist a sense of "I am" as a reference point, there automatically exist the view of "another" as the other reference point.
With this view of "I am" a comparison can be made with the "another" hence the arising of conceit at 9 levels. When one is better one makes the comparison "I am better", "equal..", "less than ..", and their permutations( *sorry couldn't find the citation").
In Khemo Sutta it has been compared to a remaining scent:
"No, friends, I do not say this 'I am' is the body,... consciousness, nor that it is other than the body,... consciousness. Yet with regard to the five groups of clinging,[1] 'I am' comes to me,[2] but I do not consider it (by way of wrong views) as 'This I am.' It is just like the scent of a blue, red or white lotus.[3] If someone were to say, 'The scent belongs to the petals, or the color, or the fibers,'[4] would he be describing it correctly?"
"Surely not, friend."
"Then how would he describe it correctly?"
"As the scent of the flower, would be the correct explanation."
"In the same way, friends, I do not say this 'I am' is the body,... consciousness, nor that it is other than the body,... consciousness. Yet with regard to the five groups of clinging, 'I am' comes to me, but I do not consider it as 'This I am.' Though, friends, an Ariyan disciple has abandoned the five lower fetters,[5] there still remains in him a subtle remnant[6] from among the five groups of clinging, a subtle remnant of the 'I'-conceit, of the 'I'-desire, an unextirpated lurking tendency[7] to think: 'I am.' Later on he dwells contemplating the rise and fall of the five groups of clinging,[8] and he sees: 'This is the body, this is its arising, this is its passing away. These are feelings,... perceptions,... mental formations,... this is consciousness, this is its arising, this is its passing away.'
"So, as he dwells thus in contemplation of the rise and fall of the five groups of clinging, this subtle remnant from among the five groups of clinging, this subtle remnant of the 'I'-conceit, of the 'I'-desire, this unextirpated lurking tendency to think: 'I am' is brought to an end.[9]
"Friends, it is like a cloth, soiled and stained, whose owners give it to the washerman. He rubs it smooth with salt-earth, lye or cow-dung then rinses it in clean water. Now though the cloth has been cleaned and thoroughly purified, there still hangs about it, unremoved, the subtle smell of salt-earth, lye or cow-dung. The washerman returns it to the owners, who put it away carefully in a sweet-smelling box. Then the smell of salt-earth, lye or cow-dung that still clung to it disappears completely.
"In just the same way, friends, though an Ariyan disciple has abandoned the five lower fetters... [as above]... this unextirpated lurking tendency to think: 'I am' is brought to an end."
TL;DR version
Sakkāya-diṭṭhi is self-view or self-belief.
Conceit or māna is self-emotion.
Long version
Identity view or personality belief (sakkāya-diṭṭhi) is the "theory of soul, heresy of individuality, speculation as to the eternity or otherwise of one's own individuality" according to Bhikkhu Bodhi. It's a wrong view or belief that one is identical with, contained in, independent of, or is the owner of, the five aggregates.
It's merely the wrong view or belief or conviction related to the self. For example, the belief in an absolute, eternal and independent self would be an example of identity view.
This is discussed in the Sabbasava Sutta:
"As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will stay just as it is for eternity. This is called a ... a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.
The statement "sabbe dhamma anatta" says that all phenomena is not self. It does not say that there is no self.
Conceit (māna) on the other hand is not just a belief or view or conviction. It is also an emotion that is deep-seated. The deep-seated fetters are harder to remove than views. Only an arahant has dropped conceit completely.
Ven. Nyanaponika Thera writes as a footnote to his translation of the Pahana Sutta:
"Conceit" refers in particular to self-conceit (asmi-mano), i.e., personality belief, on both the intellectual and the emotional levels."
According to the Pahana Sutta:
"If a monk has given up the tendency to lust in regard to pleasant feeling, the tendency to resistance in regard to painful feelings, and the tendency to ignorance in regard to neither-painful-nor-pleasant feelings, then he is called one who is free of (unwholesome) tendencies, one who has the right outlook. He has cut off craving, severed the fetters (to future existence), and through the full penetration of conceit, he has made an end of suffering."
Updated view:
Conceit in Buddhism is a technical term, referring to the deep-rooted habit or tendency of self-expression or self-clinging.
It's different from self-view or identity-view, which is more like a belief, than a habit.
The difference between overcoming self-view and overcoming conceit, is like the difference between overcoming wrong beliefs about diet and exercise, and overcoming obesity.
This video which Sankha referenced says that there are levels of perversion i.e. "perception", "thought", and "view" – and that Sakkayaditti is a view whereas Mana is a perception.
By analogy you might:
Simile:
The little boy believes in Santa Clause. At seven years of age, he discards the belief and concludes that Santa Clause is not real and never actually existed. He has eradicated the Santa Clause Personality View.
Fast forward 13 years. He puts a gift under the Xmas tree addressed to his new wife and signs it "From Santa." This came, not from Personality Belief but from conceit wherein he "compares" (I am just as good as ...) himself to Santa.
