I think that "perhaps" is more official than "maybe". :)

They mean the same, but they are not always used the same. "Perhaps" is not used very often in spoken English where I am from. Almost always, "Maybe" is used. "Perhaps" sounds somewhat poetic, and as such, it just seems a bit too much to use it in normal prose conversation. However; in written work, "Perhaps" may be used to give a bit more of a "I wonder" feel to the words. To me, it always feels a little more poetic, and a little more decorative to say "perhaps."

It's the same like in all languages there are synonymes to each word. take it easy it's possible to replace maybe by perhaps in all the cases .. " pourquoi chercher midi a 14h? "

Karim, you could also use "no 'perhapses'" in the sense that you said "No maybes." But that is a special case usage - not the normal way the words are used. I explained below, though. It is a difference in the way it feels on native speakers' ears, and as such, it is just a difference in where it gets used, but there is no real difference in meaning.

The differences between perhaps and maybe are the following Maybe is used as a noun, in phrases like no ifs, buts, or maybes. Perhaps is used in polite requests: would you perhaps consent to act as our guide? The meaning of maybe is possibly, perhaps. Except in set phrases, you can replace maybe with perhaps. As far as I know, there is no distinction in the usage of the words you describe; both the words can be used with actions.