If I can just talk about the English-language words ...
"Perceive" comes from a Latin root which means:
- "per" -- wholly, thoroughly, entirely
- "capere" -- to take, to grasp
So "perceive" means "take entirely" or "grasp all there is of it".
In English it's used metaphorically (i.e. you perceive something mentally), in French it's usually used literally (e.g. you would perceive the money for the rent when you receive it, when it's given to you).
The "con" in "conceive" comes from a root meaning something like "with" or "and" or "in parallel to" or "as a result of" -- it's used in the word "consequence" for example, i.e. it's something which exists "with" something else in a sequence.
So I think that (in English), to "perceive" is to grasp everything about (the totality) of something; and "conceive" is something separate or additional which happens in parallel.
For example if I hit something solid, if I walk into a table accidentally because I'm walking without paying attention, then there's a perception of a physical sensation (the sense of touch).
I may conceive of other things beyond that, e.g. "I am hurt, I am angry, something attacked me, I should attack in return, that table attacked me" but those are consequent to the initial perception of sensation.
I guess (not based on scripture) that "formulation" maybe includes all use-of-words. So for example, seeing green and saying "I am seeing grass" is a conception. I think that even "I am seeing green" is a conception, "I" is a conception and even the word "green" is a conception (and whatever color you're actually seeing might not be an ideal green but might instead be a bit blue or brown or etc.). Anyway maybe seeing what you see is perception, and describing it after that is formulation and conception.
The two sentenes quoted in the question seem to me the same -- I think that "formulation" and "idea" and "conception" are all more-or-less the same, all "conception" (except I don't know what the distinction is between "conception" and "sixth type of sense-object" i.e. "sense-object of the mind").
However reading The Five Aggregates -- A Study Guide that the way it's used in the canon isn't exactly as I described it above.
One thing it says (which agrees with what I said above) is that perception isn't the same as feeling. Now "feeling" is ambiguous in English (e.g. it can mean "I feel the table" to refer to the sense of touch), but when it's used as a translation of vedanā it means something like, "I have feelings about the table" e.g. "This feels pleasant" or "This feels painful". This kind of feeling isn't (or is distinguished from) perception.
But (unlike what I said above) perception does include:
- Labeling (assigning a name to)
- Recognising (e.g. shape and function of a physical object, what it's used for)
- Abstract concepts, e.g. one is able to "perceive impermanence".