[tex]|u, d\rangle[/tex]

where u mean spin-up and d mean spin-down, I know that it is a state for a system which contains two spins: the first one is up and the other is down.

But if I write the state as

[tex]|u\rangle + |d\rangle[/tex]

What does this state mean? To me, I will read there are two partilces: one spin up and one spin down, so what's the different from the first one?

It is more confuse if I write the Fock states

what does [tex]|4, 3\rangle[/tex] mean ? The first subsystem has 4 particles while the other has 3 particles?

And [tex]|4\rangle + |3\rangle[/tex] ?