For me talking in a regular conversation mags and clips are interchangeable however I make a conscious effort to say mags or clips when speaking in certain situations (eg. Gun shows, or people who actually know things about guns and would look down on me if I were to say clip when I was referring to a mag).
OP: Clips are usually strips of metal or whatever that hold a bunch of bullets such as on #4 Lee Enfields or the 1903 Springfield (and revolvers too, they use "clips" that force all the bullets into the chamber at once rather than having to hand load each bullet one by one). There is a video of a guy on youtube who speedshoots a revolver, when he reloads he uses these revolver clips. YouTube - Fast Revolver Shooting
that's the video.
They're disposable and just a piece of metal, the bullets are "open" and not contained within the magazine itself.
Mags on the other hand (eg. STANAG mags used in the M4/16) or pretty much any modern firearm use mags, they're encased in a "magazine".
Note: I'm not a gun enthusiast, I do know a little bit about them so the above might not be entirely accurate however that's the general idea and basically what I use to define a clip or a mag.