Grammar usage

There's very little (if any) difference in meaning, but usage varies.

Commence could be considered more formal, and although it is used much less in spoken language, it frequently turns up in ceremonial situations – Let the Games commence.

The nouns start and beginning often imply a different length of "commencement". The start of something is often a point in time (race, time period), whereas a beginning can refer to the first "bit" of something (book, game).

Sometimes the verbs are used in particular contexts. For instance, you wouldn't begin or commence your car – you'd start it.