... Are both of you using "API" as a synonym for "REST"?
This is the worst moment in time to talk about "REST".
Do you mean the Roy Fielding "REST" or the HTTP API "REST"?
Calling the latter "REST" is wrong. It's like calling a hermit crab a snail.
Edit: I forgot to mention, the former is gaining relevance as the elusive evolvable clients are now a thing.
Seems like in this context API means HTTP API lol
It's annoying, but that's been pretty common for the last decade. It's just like how everyone uses "REST" to mean "JSON RPC". In the end, we all basically know what the other ones are talking about, so it's pretty pointless to get bogged down in semantics.