Maybe and perhapes are both synonyms of the words probably, possibly. when we use the word maybe we refer to something that may have or may have not happened, which leaves us with a 50/50% but when we use the word perhapes it suggests that we are almost sure in a range of 70% to 80% accuracy. example1: i don't know why james haven't showed up yet, maybe he didn't find where to park the car. example2: i don't know why james haven't showed up yet, perhapes he didn't find where to park the car. As we can see in ex1: when we used the word maybe, it gave the impression that parking the car is possibly the problem or it could also suggest that something came up and kept james busy . While in ex2: trying to find a place where to park the car is most probably why james haven't showed up yet. I hope my explination was useful good luck :) .
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.