The term electron pressure is used for the pressure contribution of electrons within a material (e.g., within a star). Sometimes the phrase is meant to be short for electron degeneracy pressure (aka degenerate electron pressure), a particular type of electron pressure.
In a low density plasma, electron pressure is the contribution of electrons as particles, e.g., in a Maxwell-Boltzmann distribution: if the plasma is neutral and fully ionized, electrons may be counted as the sum of the atomic numbers of the ions and if not fully ionized, that must be accommodated, either using the Saha equation or some function that estimates it in the appropriate regime. The ideal gas law applies, counting the electrons as some of the particles. Electrons repel each other and attract positive ions (Coulomb force): if sufficiently spread, this is merely the mechanism of their elastic collisions, but if the plasma is sufficiently dense, a correction term in the equation of state (EoS) that estimates the effects can be useful.
At extreme densities (e.g., within white dwarfs), electron degeneracy becomes a factor: the electrons are sufficiently confined that per the Pauli exclusion principle, they must be at different energy levels to avoid duplicate quantum numbers at too close quarters, and increasing the density (which confines them further) requires the energy to boost some to higher energy levels, and resistance to compression provides sufficient energy, the resistance termed electron degeneracy pressure. When this degeneracy is partial (when a bit of such degeneracy is sufficient to allow the density), a correction term can be incorporated in the EoS that estimates the added effect.