The difference in FLA / FLC is just semantics.
If I asked you, "What's the FLA of that 350HP motor?", your answer would need to be just a number, such as "440" which is sometimes an inaccurate way to communicate because it can be easily mistaken for something else, as in this case possibly for the voltage. So if I say "What is the FLC of that 350HP motor?", your answer would be "440 amps", which would be less open for misinterpretation. But really, it's a trivial thing.
There is a difference between FLA and RLA however. When dealing with a piece of equipment that is designed to do a narrowly specific job, where even the slightest abuse might have effects beyond that piece of the machine, the difference may be important. So a motor that is designed for multiple uses or variable loads, such as your compressor, has an FLA rating because you don't know what it will be used for or loaded at. Another motor, such as the fan WITH that compressor, is designed to operate exactly THAT fan at an exact air delivery, so even though technically it may have the capacity to run at higher amps, to do so may have other consequences. So the rating of the motor is expressed in the maximum that it should be allowed to run at, or Running Load Amps.