When talking about “piece,” it is nothing else but the shells in a drum set. Therefore, do not think that cymbals and hardware are included in this.
And the pieces of a jazz drum set include a snare drum, bass drums, and toms.
The main difference between a four-piece and a five-piece jazz drum set is the number of toms. The four-piece has two toms (i.e., the bass drum, the snare, the floor tom, and a tom). And the five-piece drum set has three toms.
Also, more drums mean more sound possibilities, especially great fills. But it takes up more space.
A four-piece drum set is more suitable for jazz, where the ride cymbal takes the groove’s lead. It is also easier to transport.