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This title probably makes no sense, and that's the problem I'm having. As far as I know, degenerate matter is an entirely different phase of matter altogether — it may have fluidic properties, but it's very different from the traditional states of matter. It only occurs under extremely dense or low-temperature conditions.

However, Wikipedia's article on metallic hydrogen calls it a form of degenerate matter, and then says:

At high pressure and temperatures, metallic hydrogen might exist as a liquid rather than a solid

I'm completely confused. Is degenerate matter its own separate phase, or can it be in the form of a liquid or solid? Did Wikipedia just make some big mistake?

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Degeneracy just means that the fermion species (could be plural) in a substance fill up (nearly) all the available momentum states up to the Fermi energy. i.e. The occupation of energy states looks quite different to the Maxwell-Boltzmann distribution.

The properties of the matter will be influenced by the forces between particles. Also note that degenerate matter may consist of a degenerate species accompanied by non-degenerate species (e.g. in hydrogen). If the particles are pointlike and non-interacting then it can be treated as an ideal gas (note ideal, not perfect). If there are very strong Coulombic forces between the particles, they could get locked into a solid structure, but if those forces are weaker then a liquid state could exist.

Degenerate substances can be different in terms of compressibility. One normally thinks of gases as compressible, liquids as highly incompressible and solids as incompressible.

In a degenerate matter these distinctions are not clear cut at all. For example, the solid crust in a neutron star is more compressible than the neutron liquid in the interior.

There can be other differences too, in terms of heat capacity, conductivity, viscosity and so on, but these depend on details and whether degenerate species are accompanied by non-degenerate species.

So to give three examples. Degenerate matter exists as (or is usually described as): an (ideal) gas inside young white dwarfs; as part of a crystalline solid (nuclei are locked in a lattice, surrounded by degenerate electrons) in old, cold white dwarfs and neutron star outer crusts; and in liquid form in the dense neutron star interior, where strong nuclear interactions cannot be ignored.

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