They two senences mean exactly the same. It is difficult to decide what I would say myself, without a context. If I met you and you were wearing a nice jacket I would say: 'Jeg liker jakken din.' I would not say 'Jeg liker din jakke.' The last sentence would be too formal. However, they mean the same, and both are correct.
norwegian doesnt really have levels of politeness, as far as i can tell; the only thing resembling politeness that i can think of is writing in bokmål instead of in your regional dialect. that's why they dont have terms or address (mr and mrs) or polite pronoun or verb forms. for that reason, id say that 'guttens jakke' would be as formal as 'jakken til guten', and the informal way of saying it would depend on where you are in norway
Norwegian uses compounds (adding two or more words togeher). A jacket meant for boys would be "guttejakke". Jacket meant for girls would be "jentejakke" and for women "damejakke", whereas a jacket meant for men would be "herrejakke". "herre" (gentleman?) is a more formal version of "man".
It has a different meaning. The jacket on the boy doesn't show that the boy owns the jacket, just that it's on him and she likes the way it looks. Whereas the other one shows that the boy owns it and doesn't really have anything to do with how it looks on the boy (maybe she wants it for herself).
Since 'til' can also mean 'on', isn't 'The girl likes the jacket on the boy' also correct? How would one put the stress on the girl liking the jacket itself that belongs to the boy (The girl likes the boy's jacket) vs. the girl liking the fact that the jacket is worn by the boy or perhaps they way the jacket looks like on him (The girl likes the jacket on the boy)?
not really, the sentence here is showing that the boy owns the jacket, whereas 'the jacket for the boy' could imply that the boy should have the jacket but might not necessarily have it yet; also 'the girl likes the jacket for the boy' is janky and could be interpreted as that the girl is liking the jacket on the boy's behalf