The meaning of maybe is possibly, perhaps. Except in set phrases, you can replace maybe with perhaps. As far as I know, there is not the distinction in the usage of the words you describe; both the words can be used with actions.

"Perhaps" is more formal and "maybe" is more casual. "Perhaps" is common in academic writing. "Maybe" is common in conversation.

When there is a question of uncertanty in english we use the conditional. Possibily/might/maybe/perhaps. possibily I might be there tomorrow Maybe I should/maybe go there by myself Perhaps I should go tomorrow. I hope this helps.