Collisions are violations of the pairwise non-intersection constraint between bodies. Collision forces are Lagrange multipliers of these constraints. Collision normals are the (normalized) partial derivatives of the constraint function wrt one of the body's configurations.
That sounds like the kind of thing which works if you're doing physics at 1kHz+ with an integration algorithm with good numeric stability which honours conservation of energy, but in games, we're often running physics at down to 30Hz using some ad-hoc Euler-Chromer, which requires very different approaches
It's still the same principle even in games. If you are trying to explain where forces come from and how resolution works, you need to ground it in something. Otherwise you are just adding extra assumptions onto assumptions.