In the past, my understanding was always that the processes of
- dressing a bare quantity (such as mass or charge) and
- renormalizing these same properties
are different things. Dressing, as far as I had come to learn, was the result of switching on interactions in a formerly free theory and observing that polarization of the vacuum and the emergence of clouds of virtual particles, in particular short-lived particle-antiparticle pairs, would alter physically measurable quantities like mass and charge.
Renormalization, on the other hand, was to me a slightly more formal thing. At its most intuitive, I understood it to be the process of calculating the scale-dependence of couplings, usually with the intent of starting from their values within some microscopic theory $S$ valid at an ultraviolet scale $\Lambda$ and taking their flow down to some lower (usually humanly observable) scale $k$.
Of course, one reason why couplings are scale-dependent in the first place is that, depending on the scale at which a particle's charge or mass is measured, the size of the enclosing cloud of virtual particles and the resulting screening effect will be very different.
However, I recently stumbled upon several text passages that seem to indicate screening and renormalization are actually the same. For instance, Wikipedia in History of quantum field theory states (somewhat vaguely)
What we measure, and hence, what we must take account of with our equations, and what the solutions must account for, are the "renormalized mass" and the "renormalized charge" of a particle. That is to say, the "shifted" or "dressed" values these quantities must have when due systematic care is taken to include all deviations from their "bare values" is dictated by the very nature of quantum fields themselves.
Similarly, Quantum Field Theory by Tom Lancaster and Stephen J. Blundell claims
The process of renormalization may be imagined as a particle dressing itself in interactions.
So is my understanding wrong? Does it lack some important point? Or is it simply that these terms aren't very rigorously defined or that their usage lacks consensus?