Learn English – Differences between “pig” and “hog”

The New Oxford American Dictionary has the following note.

For complex historical reasons, prove developed two past participles: proved and proven. Both are correct and can be used more or less interchangeably: this hasn't been proved yet; this hasn't been proven yet. Proven is the more common form when used as an adjective before the noun it modifies: a proven talent (not a proved talent). Otherwise, the choice between proved and proven is not a matter of correctness, but usually of sound and rhythm—and often, consequently, a matter of familiarity, as in the legal idiom innocent until proven guilty.

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.