This is what understand about an API, and this what I tell myself.
Forget about first two terms, just focus on interface. What an interface? It's an medium to connect two or more things which wants to communicate. You using your phone, TouchPad is that interface. For client and server architecture Urls or endpoints are an interface.
So, I have been forgetting the two terms. Some days ago I explained that to someone How I take them, but that someone asked-
What is the meaning of the two terms if they are there to be ignored?