You are overthinking this. There really is no difference between the two words, and no situation where one would be appropriate and the other wouldn't. It certainly has nothing to do with the position in the sentence - you're making all this far too complicated! 'Perhaps' is possibly fractionally more formal, and used a tiny bit less in speech than 'maybe' is, but it's nothing worth worrying about. You can use either word in any situation.

The two words are synonymous and 99% interchangeable. "Maybe" is heard more frequently in US English conversational speech. I think there are a couple of situations where one cannot be substituted directly for the other: 1. Game of Thrones is perhaps the best show on TV. = Game of Thrones may be (NOT maybe) the best show on TV. = Maybe GoT is the best show on TV. 2. The responses included 20 "yeses", 5 "nos", and 2 "maybes" (NOT "perhapses") 3. There's a fixed idiom/slang phrase, "definite maybe" which is very difficult to translate: + Are you coming to my party? - That's a definite maybe! (<= I don't want to say "no", or I don't want to commit to an answer)

well as with most things there are 2 answers . 1 the short one, yes they basically have the same meaning in common usage today. Though they get used differently in some contexts. 2. They do have a slightly different meaning. perhaps has been in usage since at least the 1800s it has been in decline but consistently used. It comes from per haps. or to use modern words by luck. maybe is a much more recent word only really used since the mid 1900s at least in liturature. It comes from "it may be that". So the difference is that with perhaps you are stating a preference for an outcome where as with maybe you are acknowledging a possibility. as such you could say this is why it may be used in more polite forms of speech especially when asking for a favor. perhaps you can help me , is effectively if I am lucky you can help me. which may show you will value the help more, as such could be considered more polite. maybe you can help me, is just it may be that you can help me. This is just dispassionately observing that the possibility exists that you can help me. How many people are aware of this difference, is not something I can say. I am something of a pedant as I like to be able, to utilise words to their best effect but its not necessary.