A. Neumaier said:
The point is that the quasi vacuum defined by the Fermi surface depends on temperature, hence one has a different sector for each temperature. The standard vacuum corresponds to zero temperature.
In more physical terms, here the ground state is called ground state, and the vacuum is always the state with no particles present.
In a many-body system in thermal equilibrium often you can describe the system in terms of "quasi particles". These describe usually collective excitations of the ground state but look similar to "particles" in the Green's-function formalism, and different phases of a system are characterized by different kinds of "thermodynamically relevant quasi-particles".
E.g., in a Fermi liquid you can have a "normal phase". There you have a "ground state" which is filled up to the Fermi level, and quasi-particle-like excitations which may look like the "real particles" but with a different mass. Also holes in the Fermi sea can look like quasi particles with the opposite charges. Then you can have bound states of holes and particles ("excitons") etc. etc. Other quasi-particle-like excitations can be also of bosonic nature, e.g., phonons, plasmons, etc.
Phases are usually characterized by an order parameter. E.g., in the normal phase of a Fermi liquid, you have ##\langle \psi \psi \rangle=0## but if there is any (effective) attractive interaction between the Fermions at sufficiently low temperatures the ground state is no longer a Fermi sea but also Cooper pairing occurs, where ##\langle \psi \psi \rangle \neq 0##, and the Cooper pairs (which are pairs of two electrons close to the Fermi surface with opposite momenta and usually also opposite spin) become quasi-particles too. A specialty here is that the non-zero order parameter describes an electrically charged state (with ##q=-2e##) where the charge is the electric charge, i.e., coupling to the electromagnetic field, i.e., the symmetry under multiplication with a phase factor is a local symmetry, and thus you have no spontaneous symmetry breaking but a "hidden local gauge symmetry" aka the "Anderson-Higgs-Brout-Englert-Kibble-et-al mechanism", making the corresponding gauge field, i.e., here the photons, massive. This explains the Meisner effect.