I agree with all of the answers so far. I want to note that in American English, we rarely use "perhaps" in writing or speaking. "Maybe" is our common word for both. In a sentence, we may also insert "possibly" or forms of "possible" instead. Perhaps he may change his ways, if he falls on his face. Maybe he will change his ways if he falls on his face. If he falls on his face, it's possible he may change his ways. Hope this helps! :)

Perhaps is a more formal way to say maybe. Maybe is more casual and much more likely to use daily.

I think there´s no difference between those words. I mostly use "maybe". The only mild difference I can come up with is that I haven´t ever heard or read "maybe" in a formal context. If I were to write one of these words in an essay, I would write "perhaps".

Both have the same meaning, I do however see 'maybe' being more used than 'perhaps'