API vs REST API – Software Engineering Stack Exchange

I recently posted that question:
Rest API for multiple applications?
and after searching a little bit more and reading that question:
I basically want to ask that:
How would I choose between an API and a REST API? why should I prefer one and not the other?
I am asking in general if there is a general answer, but I will also give a specific example. So from what I understood from the two questions above, both a REST API and a API can be use by multiple applications (pc app, android app, web app etc), so if I want to create the back-end that will share all these apps (pc app, android app, web app etc) at the same time, so all these apps will exchange information with the back-end and the back-end will also store all this information, then is there any deference in which one will I choose? Even if there is no deference, which one should I choose and why?