As a term, 'instance' is already baked into code, databases, and APIs.

If I wanted to use an API to block 'lemmy.world', for example, I'd call 'site/block' with the relevant 'instance_id'. That's already 2 different terms for the same thing ('site' and 'instance'), which isn't great, but adding 'provider' into the mix means you're now saying "if you want to block a 'provider', use the 'site' endpoint with the ID for the 'instance'", which is arguably worse.