Learn English – the difference in usages between “send” and “dispatch”

maybe is an adverb, meaning perhaps or possibly.

may be is a verbal construction, formed of the modal verb may and the verb be, which can be used in sentences like “he may be in the office today”. Note that, if you were to rewrite this sentence with maybe, you would say “maybe he is in the office today”. Because maybe is an adverb, you need to add a verb to the sentence (is, a form of be, in that case).

Surely there should be more of a difference between the two words. If they mean the same thing surely there would be no need anymore for two words

There are a lot of near synonyms in English, so this does not follow at all. It's particularly so when you consider that act entered the English language in the late Middle English period, from French, while deed was in the language from the very beginnings of Old English. Many, but not all, seeming redundancies in English vocabulary have a similar origin story.

It is true that there are differences in nuances. The primary one would be that an act would generally be need to be relatively remarkable before we would use the term deed. One can do a particularly brave or noble or dastardly or evil deed, but one can't really do a lazy or everyday or common deed. There's nothing technically wrong with the latter, but it wouldn't be an idiomatic use.

There are similarly some differences in what verbs and prepositions are used with either. One doesn't do an act, one cannot be in the deed of anything.