If I'm understanding what you're asking, it's not "how the file is being played," but what kind of file it is, i.e., if you have an mp3 file extension, when you hit play, you're playing an mp3 and likewise for flac, ape, aac, whatever you have.
The main distinction you're after, I think, is between lossy and lossless files. Early digital music (say from iTunes) was all encoded in lossy formats to save space. aac was Apple's goto, though other sites used mp3, which is also lossy (or current Spotify which uses ogg vorbis). What "lossy" basically means is that something has been removed from the file to make it smaller (and thus make it not quite CD quality), but that something is supposedly inaudible, especially at high bit rates, e.g., an mp3 with a bitrate of 320 kbps is supposedly sonically indiscinct from a lossless (CD quality) file. However, many claim to be able to hear the difference in blind tests, and of course, the better your equipment, the greater the chance you might hear a difference. Whether that matters to you or not is another matter.
When you rip a CD in MC or elsewhere, you can choose an encoder: a lossy one like mp3 or ogg vorbis or a lossless one like flac, alac, or ape. I think the majority of users on here rip their primary version losslessly and then when they want a lossy version for portability on a phone or thumb drive, they make a second version of the file through a conversion to a lossy format for space. Obviously, these days one can also buy a lot more lossless files online at places like Qobuz or Apple Music and even get hi-res lossless, which is a topic for another day.
There are more technical ways to talk about lossy vs. lossless, but that's the basic difference.