When someone says "degeneracy pressure", then I would assume that they mean the ideal degeneracy pressure felt in a gas of non-interacting, indistinguishable fermions, simply due to their non-zero kinetic energy.
The expression for ideal degeneracy pressure (e.g. for non-relativistic fermions)
$$P = \frac{h^{2}}{20m}\left(\frac{3}{\pi}\right)^{2/3}\, n^{5/3}\ , $$
where $n$ is the number density of fermions of mass $m$, does not involve: charges, baryon numbers or any interaction constants associated with any type of force. It is a purely quantum mechanical effect that requires densely packed fermions to have non-zero momentum. The only force involved actually is gravity, which provides the potential that confines the fermions and hence quantises the momentum states.
It is a fair statement to say that white dwarfs are "supported by electron degeneracy pressure". That is because the Coulomb interactions between the electrons and nuclei, which are included in any proper treatment of a white dwarf's structure, are a very small perturbation to the equation of state, reducing the pressure by just a few per cent.
A neutron star however, or at least all the neutron stars found so far in nature, cannot be supported by ideal neutron degeneracy pressure (NDP). The interaction terms between the nucleons completely dominate the equation of state.
One of the first papers to discuss the possibility of neutron stars, by Oppenheimer & Volkoff (1939), showed that ideal neutron degeneracy pressure (NDP) can only support a stable ball of neutrons up to 0.75 solar masses. i.e. the "Chandrasekhar limit" (but using General Relativity) associated with NDP is only $0.75 M_\odot$; and all measured neutron stars are more massive than this (the least massive known is about 1.17 solar masses - Martinez et al. 2015).
To support more massive neutron stars or halt the core collapse in a supernova requires interactions between the neutrons, or the neutrons to turn into something else like a quark-gluon plasma. This interaction can be provided by the strong nuclear force, which (in broad terms) is attractive over ranges of $1-2 \times 10^{-15}$ m, but strongly repulsive if you try to squash nucleons closer together than this. The details of this interaction in a neutron star are still uncertain because of the relativistic many-body nature of the problem and that the nuclear matter is highly "asymmetric", in the sense of there being just 1 proton for every 100 neutrons.
The above terminology and use of language is entirely consistent with statements by the leading researchers in neutron star and core-collapse physics. e.g.
Lattimer & Prakash (2001) in "Neutron Star Structure and the Equation of State":
the
pressure near the saturation density is primarily determined by the isospin properties of
the nucleon-nucleon interaction, specifically, as reflected in the density dependence of the
symmetry energy, Sv(n).
Woosley & Janka (2005) in "The Physics of Core-Collapse Supernovae":
Eventually the repulsive
component of the short-range nuclear force halts the collapse of the inner core when
the density is nearly twice that of the atomic nucleus, or 4–5 × 1014 g cm−3.
Ozel et al. (2016) in "The Dense Matter Equation of State from Neutron Star Radius and Mass Measurements":
Our understanding of the equation of state in the vicinity of the nuclear saturation density is firmly founded on
nucleon-nucleon scattering experiments below 350 MeV and on the properties of light nuclei. An approach that makes
use of these data most directly is based on describing the interactions between particles via static two- and three-body
potentials at this density...
And so on...
