Yup. There are actually three that are most seen, sharp, half-sharp and sweet, but the first two are only available from those that deal especially in paprikas and from some of the better spice retailers.
Imo, paprika does not hold up at all to long dry heat cooking (which is why I don't use it in rubs, unless I need a filler; I find it near-flavorless); it's better suited for shorter cooks or for moist cooking (like braises, sauces, etc.).
Smoked paprika is nice for quicker cooking grilled items that are not likely to be in smoke long enough to take on much. It's also nice in sauces where one desires smoke flavor but wants to avoid the (horrid, imo) taste of Liquid Smoke.