Specific to performance, swing is a type of timing which some define as dividing each beat in to three pieces and then playing the first and third part of that division. However many would fault this definition, claiming that swing is a "feel" that is not precisely divided into three, or four, or two, but some vaguely specific timing where the beat is divided somewhere between that and a rhythm of dotted eight - sixteenth note paring. I hear it as very close to the latter (dotted eight - sixteenth note) but the triplet(divided into 3) feel is still there somehow. Listening to some swing examples and then coping the rhythmic feel is a good way to get an understanding of what it is. Sometimes I interpret swing differently depending in part on the context(is it jazz? Is it slow, Is it fast? etc.), and my mood.
Note that when a composer writes two eighth notes in a piece or section that is indicated to be swing, the composer could intend for you to actually play the rhythm I describe above. Just as often as not, it could also be written as dotted eighth - sixteenth note pairs.
Shuffle is similar to swing but more dotted eighth - sixteenth perhaps even a little late on the sixteenth..... but this is up for debate.
None, or "straight" would be an instruction to play rhythm exactly as written.
There are many many styles and cultures in the world. and many (not all) of them are basically either swing or straight with a little extra context or subtlety.
Stride might be another good style to look into.