What is the difference between photons from an electron and photons from a proton?

The description of EM in terms of (virtual) photons is very good for describing/predicting scattering cross sections and decay rates, which is what particle physics deals with most of the time.

It is not very good at describing attraction and repulsion - which is the first thing people think about forces in everyday life.

So for something like Rutherford scattering the first order cross sections for electron-proton scattering and positron-proton scattering, involving interchange of one virtual photon, are exactly the same. There is a factor $Q_1 Q_2$ in the amplitude which is $+1$ for $e^+p$ and $-1$ for $e^-p$, but this is squared to get the probabilty.

If you go to second order, exchanging two photons, the factor in the amplitude is $(Q_1 Q_2)^2$, even less promising. But the interference term between the two amplitudes is now $Q_1^3 Q_2^3$ so this does produce a difference between the two charges.

Extending this to many orders, such differences produce the attraction/repulsion result which is the main feature of everyday electrostatics.

So: the virtual photons from positive and negative charges are the same. But the way in which they interfere with other virtual photons involved in other exchanges produces, eventually, an attraction/repulsion difference.