They're both modules (addons, if you want) that plug into DCS World.
Difference is that A-10A has simplified systems with no clickable cockpit and only keyboard commands while A-10C is full blown click-everything hardcore sim. Also, two airplanes are different in a lot of things. A = old model, steam gauges, somewhat simple. C = new model, multifunctional displays, targeting pod, laser guided stuff and much more.