Even though people use the words inconsistently, those people who distinguish them at all do so consistently, and you can use cognates to remember which is which: ‘sense’ = ‘feel’, so ‘sentient’ = ‘feeling’; ‘Homo sapiens’ = ‘wise man’, so ‘sapient’ = ‘thinking’ (more literally ‘discerning’ in the Latin).

I usually take it for granted that snakes are sentient but not sapient, although I don't really know enough about snakes to be sure of either.

But there's another idea, neither of which these words quite captures, that seems to be what really matters to Harry: self-awareness (‘anything that lives and thinks and knows itself’). A snake may sense its prey, but does it sense itself? It may discern that its prey is food, but does it discern that its self is a self?