There are several sorts of plasmas. An ionized gas is a sort of plasma, also called thin plasma.
Thin plasmas, while physically different from a metal, share a surprisingly large number of properties with it:
- They both have two separate charge carriers, cations and electrons.
- On both, the cations have a negligible contribution to current and the electrons form a gas.
- They have similar dispersion relations (leading to similar "local" Ohm's law in both).
It's because cations don't contribute much that they seem similar, in spite of one being a gas and the other a solid.
When you heat a thin plasma, for a while it's still an ionized gas. As it gets hotter, you get the energy to rip more and more electrons from atoms, but the nuclei remain untouched. However, cations start to contribute more so properties differ noticeably from a metal. It's the field of magnetohydrodynamics.
When a plasma is hot enough to rip nucleons from the nucleus, it becomes a thermonuclear plasma, and its properties change again. This is the sort of plasma the Sun is made of.
Heat such a plasma again (a lot!) and you have the energy to rip quarks and gluons from the nucleons. This is the quark-gluon plasma.
Overall, you get a different sort of plasma each time you become able to extract a new sort of particle from the system. The similarity with a metal only exists at low energy.