I see two Pali words which are translated into English as "intention":
Do these two words mean exactly the same thing? If not, what is the difference?
In Pali “Sankappa” means conscious thoughts that involve “san” or things that contribute to the sansaric journey (rebirth process). Here “sankalpanä” comes from “san” + “kalpana“, where “kalpanä” means conscious thoughts. In my native Sinhala language when one keeps thinking about something, these thoughts are called “sankalpanä“. Samma sankappa means removing unskillful conscious and deliberate thoughts, and cultivating skillful, moral thoughts. If one is ever mindful of the generation of either greedy or hateful conscious thoughts, and practice this over time, then one can eventually put a stop to them. This is the basis of both Mindfulness of Breathing (Anapanasati) and Four Foundations of Mindfulness (Sathara Satipattana) meditations.
Cetana can be translated as “intention” and as “volition”. Volition incorporates “more personal attributes”. Neither translation gives the full meaning of this Pali word, if you go into Abbidhamma. It says that many mental factors come into play for Cetana to arise. Intention arises when a certain group of mental factors become dominant. Some mental factors are moha (ignorance), Ahirika (shamelessness), Anottapa (fearlessness in wrong), uddhacca (restlessness or agitation), lobha, ditthi, vicikicca, etc. For instance, a person may lie to you due to greed (lobha); or it may be due to hate (dosa); the consequences are worse for the latter. Thus cetana is not “intention” per se; it depends on how that determination came about. The Buddha said: “cetana ham Bhikkave kamman vadami“. Thus, what determines the type of kamma is the cetana. How that particular intention came about depends on the set of relevant unskillful mental factors.
Cetana is executed by action, speech and thinking.
So the difference is Cetana includes speech and action where as Sankappa by itself only includes thinking.
Please note that "Right" here is explained properly by Samma Ditti and doesn't mean right action in general sense (eg. Teaching, Nursing).
It is a mistake, because there are not enough word to translate pali to english. Translation is very dangerous, be careful. I often say, and I will keep to say until we will realize how is weak, which cause of uncountable problems, of our study system when compare to the ancient study system.
I have asked something about mind-factors similar to this question to pa-auk sayadaw, he said "you have to attain jhāna, before you can understand the answer of this question." Because the question is about mind, citta, and mind factors, citta-sampayutta, cetasika, which is easy to understand for the people who attained mind-purification, citta-visuddhi. But it is very hard to understand for people who has not enough experience in mind-developing, citta-bhāvanā, to go to the goal, mind-expert, citta-visuddhi, which can control to avoid unwholesome-citta-sampayutta and to arise wholesome-citta-sampayutta.
But if you are already attained jhāna, this is the answer:
It depend on context, mostly should describe like path of purification, which I quoteed below, but if not we can notice by each context of saṅkappa, or see in atthakathā, which always describe the weird word.
In the path of purification (I have not read the translated what I quote. I read just in pali and thai translation. Please read on your own risk):
Part 2: Concentration (Samádhi) page 136:
- So far the factors abandoned by the jhána have been shown. And now, in order to show the factors associated with it, which is accompanied by applied and sustained thought is said.  Herein, applied thinking (vitakkana) is applied thought (vitakka); hitting upon, is what is meant. 25 It has the characteristic of directing the mind on to an object (mounting the mind on its object). Its function is to strike at and thresh—for the meditator is said, in virtue of it, to have the object struck at by applied thought, threshed by applied thought. It is manifested as the leading of the mind onto an object. Sustained thinking (vicaraóa) is sustained thought (vicára); continued sustainment (anusañcaraóa), is what is meant. It has the characteristic of continued pressure on (occupation with) the object. Its function is to keep conascent [mental] states [occupied] with that. It is manifested as keeping consciousness anchored [on that object].
Part 3: Understanding (Paññá) page 470:
- (ii) It wills (cetayati), thus it is volition (cetaná); it collects, is the meaning. Its characteristic is the state of willing. Its function is to accumulate. It is manifested as coordinating. It accomplishes its own and others’ functions, as a senior pupil, a head carpenter, etc., do. But it is evident when it occurs in the marshalling (driving) of associated states in connection with urgent work, remembering, and so on. 
And you can see in saṅgaha also:
- Vitakka -
Vi + Ö takk, to think.
It is difficult to suggest a suitable rendering for this Pāli term which assumes different meanings in the Suttas and Abhidhamma.
In the Sutta Pitaka it has been employed in the sense of notions, ideas, thoughts, reasoning etc. In the Abhidhamma it is used in a specific technical sense.
'Lifting' of the concomitants to the object (abhiniropana) is its chief characteristic. As someone ascends to the king's palace depending on a king's favorite, relative or friend, likewise consciousness ascends to the object depending on vitakka (Atthasālini, p. 114).
Vitakka may well be defined as the application of the concomitants on the object. Manasikāra, as stated above, is the directing of the concomitants to the object. The distinguishing characteristics of these two cetasikas should be clearly understood.
Different values are attached to vitakka when it is used in different connections.
As an ordinary particular (pakinnakā) mental state it is simply called vitakka. When it is developed and cultivated it becomes the foremost factor of the First Jhāna. Then it is termed appanā because the mind is steadfastly fixed on the object. The ordinary vitakka simply throws the mind to the surface of the object.
In the subsequent Jhānas vitakka is, however, inhibited, owing to the habitual association with the object.
A villager, for instance, who visits the king's palace for the first time, needs the introduction of a favorite courtier. For his subsequent visits no such introduction is necessary as he is acquainted with the place.
It is this developed appanā-vitakka that is known as samādhi or concentration.
When vitakka is present in the Supra mundane Path Consciousness (lokuttara magga citta) it is termed sammā sankappa (Right Thoughts) because it eliminates wrong thoughts and applies the mind to Nibbāna.
Vitakka is used in entirely a different sense when used in connection with the temperaments of individuals. Vitakka carita means one of a discursive temperament. (See Ch. 1. note 38.)
- Vicāra -
Vi + Ö car, to wander.
Like vitakka, vicāra too is employed in a technical sense in Abhidhamma.
Vicāra is the continued exercise of the mind on the object.
Examination (anumajjana) is its chief characteristic.
So far the renderings for vitakka and vicāra are initial and sustained application respectively.
Both terms should be distinguished. Like a bee alighting on a lotus is vitakka, like its gyrating around the lotus is vicāra. Like the flapping of a bird about to fly is vitakka, like its planning movements in the sky is vicāra. Like the beating of a drum or bell is vitakka, like its reverberation is vicāra. Vicāra is also a Jhāna factor. It inhibits vicikicchā (Doubt or Indecision). (See Ch. 1. note 39.)
And for cetanā:
Both cetanā and citta are derived from the same root Ö cit, to think.
In the case of citta - mind or consciousness - the root assumes the meaning of discernment (vijānana), while in cetanā it is used in the sense of co-ordination (abhisandhāna) and accumulation (āyūhana).
According to the Atthasālini and Vibhāvini Tīkā cetanā is that which co-ordinates the mental states associated with itself on the object of consciousness. (Attanā sampayutta-dhamme ārammane abhisandahati). Like a chief disciple, or like a carpenter who fulfills his duties and regulates the work of others as well, so does cetanā fulfill its own function and regulate the function of other concomitants associated with itself.
A further explanation has been offered. Cetanā is that which arrives at action in conditioning the conditioned. (Sankhatābhisankharane va byāpāram āpajjatī'ti cetanā). Cetanā is that which plays a predominant part in all actions, moral and immoral.
Shwe Zan Aung says that according to Ledi Sayadaw, the Burmese Abhidhamma scholar, "Cetanā acts on its concomitants, acts in getting the object, and acts on accomplishing the task, i.e., determines action." (Compendium, p. 236).
The most significant mental state in the Mundane Consciousness (lokiya) is this cetanā, while in the Supra mundane it is paññā, wisdom or insight. Mundane thoughts tend to accumulate Kamma. Supra mundane thoughts, on the contrary, tend to eradicate Kamma. Hence cetanā in the supra mundane consciousness does not constitute Kamma. Cetanā in every moral and immoral type of mundane consciousness, on the other hand, is regarded as Kamma. Although Cetanā is found in Vipāka types of consciousness too, it is of no moral significance as it lacks accumulative power.
It is this cetanā that is alluded to as sankhāra and (Kamma) bhava in the Paticca Samuppāda. In the pañcakkhandha, by sankhārakkhandha are meant the fifty mental states, excluding vedanā and saññā, with cetanā as the foremost.
From a psychological standpoint cetanā determines the activities of the mental states associated with it. From an ethical standpoint, it determines its inevitable consequences. Hence where there is no cetanā, there is no Kamma.
Hi in regard to Sminda Sirinath, I noticed he somehow connected the root San , in sankalpa with sansara, but the spelling is incorrect the sanskrit word is sam, samsara. Good luck in the future. P.S. I am investiagationg the term Sankalpa, because I came accross the term in the Yoga tradition which was translated as resolve or aspiration or dedication, which I found interesting . So now, I think the buddhists have been under playing or under emphasising this term, sankalpa. which I think is a big deal , in the beginning of our aspiration or even also at the beginning of each day, or the beginning of each practice session. Good Luck everyone. Buddha indeed, does love us all, totally and forever. Never give up on your Good aspirations.