A slip strike is done by allowing line to slide out (slip) through the rod guides as you raise the rod to set the hook. This is generally done to protect light tippets and fine wire hooks from too much stress. For situations where you have a straight line to the fish, you may want to slip several feet of line out the rod guides as you strike, thus striking only with the springy, weak tip of the rod. This also puts the rod in a good position to help reduce strain on the tippet as the fish makes its initial run. For situations where you already have slack on the water, you won't need to slip nearly as much. If you don't have any slack to slip, you can always just allow line to spool off the reel as you raise the rod.
Strip striking is quite a bit different from slip striking. With this technique, you actually strip line in as you raise the rod. This can have two purposes. The first is that it reduces extra slack on the water, which otherwise may have prevented you from setting the hook properly. The second strip strike purpose is to really put the hook home (possibly even turning a fish's head if need be). By stripping a straight or nearly straight line and setting with the butt of the rod, you put on near-maximum pressure (short of a straight pull). This can be of great benefit when you need to set the hook in plate-mouthed species like tarpon. Such hook sets can be accentuated by pulling the rod and line away from each other like opening a set of scissors (often called the "scissors strike").