Is there a difference between the speed of light and that of a photon?

In quantum mechanics a particle can be treated as a wave and a wave can be treated as a particle. This is the notorious wave particle duality. I won't go into this any further here because it's been discussed to death in lots of previous questions. Search this site for wave particle duality if you're interested in finding out more.

Anyhow, assuming I interpret your question correctly you're asking if the speed of the particle, i.e. the photon, is the same as the speed of the light wave. And the answer is that yes it is. However this is actually rather unusual and in fact it only applies to massless particles like photons. If you take particles like electrons that have a non-zero mass then the wave velocity is not equal to the particle velocity.

The reasons for this get very technical very quickly, and I'm guessing you don't want to go into all the gory details. In brief: we associate two velocities with a wave, the phase velocity and the group velocity. At the risk of oversimplifying, the phase velocity is the velocity associated with the wave and the group velocity is the velocity associated with the corresponding particle. For any massive particle the two velocities are different, but for a massless particle they are the same. That's why the speed of the light wave is the same as the speed of the photon.

Comment to the question (v4):

It seems relevant to mention that there in principle could be a difference between the universal speed limit constant $c$ (which is usually casually referred to as the speed of light in vacuum), and the actual speed of light in vacuum if the photon has a rest mass, at least from an experimental point of view. Of course, no non-zero rest mass of the photon has been detected so far. See also this Phys.SE post and links therein.