Not quite.c is the speed of light in a vacuum. It's more accurate to say c is the speed of causality.

Velocity/speed isn't very useful with photons either - its a wave-particle.

Light in changing mediums is a separate but related phenomenon. The photon essentially doesn't continue on its same path, it gets absorbed by the particles in the medium. This leads to changing states (of usually an electron in an atom) which may emit another photon, remain stable but increase the atom's kinetic energy (I can't remember how likely that is, if at all), or it may eject the electron, ionizing the atom. In any case, the state changes, because the whole system (the atom, electron, and photon) can't have net energy gain or loss.