Proton vs parton centre of mass frames of hadron-hadron collisions

I am struggeling understanding a sentence from Modern Particle Physics by Mark Thompson. He states, in the chapter regarding hadron-hadron collisions (ch. 10.9, p. 275) that "the collisions take place in the centre-of-mass frame of the pp system, which is not the centre-of-mass frame of the colliding partons."

This confused me quite a bit. I get that the centre-of-mass frames of the two partons involved in the reaction, are different from the centre-of-mass frames of the two protons colliding, but I don't understand that the collisions take place in one centre-of-mass frame, and not the other. Please help me understand what he means by this.