API is in effect an interface; nothing more if you're not a programmer. For some busineses, though, the API is the entire programmed out version of what they do; it is what separates one weakly programmed bunch of code from a far superior pile of code and programmers.
It is accessed by a GUI, and you can connect via FIX. Effectively, treat that as looking at a front end (a GUI) connecting to an API (via a normal proptocal or junction, even) and doing that, as well as going out to the markets/ECN's via FIX. It just sounds difficult.
It's not.