Shocks and struts are pretty much the same thing. Usually when I hear you need your "shocks" replaced, it indicates that the shock is independent of the spring. A "strut" assembly indicates that the damper (aka shock) is coupled with the spring. Meaning that to get to the damper you have to remove the spring. If you just have a shock set up on your car, you can remove the damper without even messing with the spring. That's why when you go to the shop, it costs 2 to 3 times more to have your struts replaced. As said above (to my knowledge anyway) a "coilover" in the import world usually means height adjustable springs which install over your damper (strut set up). This is to the best of my knowledge, so if I am just way off, so be it, somebody correct me or back me up.
Thanks,
Air