is the Z boson one entity or are there as many entities as decay pairs, but they are equivalent and lumped together just wondering if it is a distinction without a difference - it seeming a bit weird that one thing can decay into different things.
 A: No more weird than that a single particle can take different paths through different slits with different amplitudes.    In this case it's mutually exclusive different decay channels.  And yes, on occasion there can be interference between them.    An excited atom can also decay through different channels to different final states in the same way.
A: I can offer a different way to think about it. Many different particles are electric charged, right? Do you think this is strange?
Well, the same happens with the weak nuclear force. Many different particles are charged under this force and, therefore, interact via a Z boson.
The only thing is that the Z, different from the photon, has a non-zero mass. So you start thinking about it more particle-like than the photon, because when it is mediating an interaction it can come as close to the mass shell as one want. But that's not always a very good way to interpret it.
Anyhow... the idea is that many things are charged under the weak force. And there is nothing odd about it.
A: There is only one Z boson. If there were more, it would change the decay rate for Weak interaction. If there were a different Z boson for electrons and muons, for example, then you wouldn't have a Z boson linking electron lines to muon lines, and this is possible.
The number of different types of particles are meaningful in quantum field theory, because the total amplitude is the sum of the different ways, and if there are different particles which contribute, it gets added up. There is a qualitative difference between "same particle" and "different particle with same properties" in QM.
This has nothing to do with Bootstrap or field theory. There is only one Z.
A: A closer similar weirdness is that a particle can have different charges, eg colour and electric, and then interact via the exchange of different particles. Worse, a charge for a non abelian force (such as colour, or also electroweak theory itself) immediately has different particles for the same charge.
So there is not problem here. It is perfectly possible for an elementary Z to decay into different pairs, and in fact it does with the probabilities predicted in the standard model. 
