What's the difference between a meson and a glueball?

This is a good question, and the basic answer is "there is no rigorous difference" (which is the main problem with experimental efforts to identify glueballs).

1) Electrically charged states, or neutral particles that are part of an isospin multiplet are clearly mesons. This means your question can be narrowed down to distinguishing isospin singlet mesons from glueballs.

2) Historically, what people tried to do is find states that are "unusual" in some way. States that do not fit into the quark model classification, states that are preferentially produced in "gluon rich" environments, like $J/\psi$ decays, or states with unusual decay patterns. (This has not led to an unambiguous discovery).

3) A more modern method is to look for isosinglets, and then try to match a lattice QCD calculation to the observed spectrum. On the lattice you can check whether a given states preferentially couples to $\bar{q}q$ or $G_{\mu\nu}G^{\mu\nu}$ operators. This is an ongoing effort.

4) On the lattice you can also study the dependence of isosinglet masses on the quark masses. If the masses are infinite then all states are glueballs. As you reduce the quark masses new states appear that at large mass scale linearly with $m_q$. These are mesons. Now you can try to follow the mesons to the physical point (this is not so straightforward because of level crossing and miixng).