Type 1 malfunction: slide in battery, gun doesn't fire. Might be caused by a failure to feed (slide did not pick up a round and carry it into the chamber, perhaps because magazine is not seated) or a failure to fire--a misfire. Solution: Tap, Rack, Assess (or Fire)
Type 2 malfunction: slide not in battery because a case is stuck in the ejection port, often called a stovepipe. Caused by a failure to completely eject, perhaps due to limpwristing. Solution: wipe the case out of the ejection port with your hand, Tap, Rack, Assess.
Type 3 malfunction: Slide not in battery. Empty case in the chamber, slide trying to feed a new round into the chamber occupied by the empty case. Also known as a double feed. Cause: failure to eject. Solution: Lock the slide, eject the magazine, work the slide 3-4 times, reload with a new magazine, Tap, Rack, Assess.
Hope this clarifies things a bit.