They mean the same thing and there is no difference in formality.

I personally feel perhaps is better one & more formal. One can be replaced by another one anytime.

The meaning of maybe is possibly, perhaps! HA! :) My answer: Maybe can be used as a noun, in phrases like no ifs, buts, or maybes... and perhaps can't. Perhaps is more often used in polite requests like, "Would you perhaps consent to be my Spanish teacher?" But generally - yup - they are the same. :D

There is no more difference between the two words than there is between quizás and tal vez. They are essentially the same. I cannot think of a situation where one would be more appropriate over the other.

same