When do we use τίποτα vs. κανένα? Is it as simple as nothing vs. no one, or is it deeper than that?
Yes, I think it's as simple as nothing vs. no/no one. We use κανένα when we refer to something countable. It's a pronoun: κανένας (m) - καμία (f) - κανένα (n)
See how it resembles ένας, μία, ένα!
Also the word καθόλου for uncountables or plurals. And τίποτα as the general "nothing".
They are used in negative sentences.
Examples: Δεν έχω καθόλου λεφτά - I have no money / I don't have any money.
Κανένα παιδί δεν πήγε σχολείο σήμερα - No child went to school today.
Δεν έχω φάει τίποτα όλη μέρα. - I've eaten nothing all day / I haven't eaten anything all day.