On what basis is the final number of units of a given cryptocurrency selected? Is the fact that a given coin will have 280 million units in some way explainable, e.g. due to some mathematical requirements or is it just a whim of the creators of a given project?
Max supply is how many tokens can ever exist. It's selected arbitrarily, and you don't even need to have it (e.g. USDT - it can be minted up to the integer limits). Often I see tokens picking a round number like 1000000000 for simplicity.
Total supply is the number of currently minted tokens. How you mint them is also entirely up to you.
Circulating supply is the portion of total supply released into the public.
Since you can code your token however you want, these notions can have different meanings for different tokens.
If your tokens can be burned, then you could say total supply = minted - burned.
Or total and max supply can be mostly meaningless if you mint your tokens dynamically.
Even circulating supply can be of questionable meaningfulness on its own (e.g. rebase tokens, like AMPL).