Resistive is an older touch-screen style. It calls for more direct pressure from the user. It is cheaper to make and any kind of stylus should work with it.
Capacitive screens are more common in today's phones and popular tablets. They usually do not need much pressure at all and chances are, you've dealt with one before. They have multi-touch support but DO need a special kind of stylus. Capacitive tend not to operate well in cold conditions and they're more expensive, but generally, capacitive screens are viewed as superior to resisitive.