Yes. Each of us has one face, which has its own appearance. That appearance changes a lot of times, not only over the long term as we grow and age, but also from moment to moment, as viewpoints change, the lighting around us changes or as we change our facial expression or talk.
There's an awful lot of variation, and this is a problem. What you're trying to do, of course, in the context of facial recognition, is to establish which of the people you know or have stored in some database you are looking at right now. That variability is difficult to overcome. You're always in the position of not knowing whether the image you have before you could count as one of the people you know or it is somebody new.
I think the variability is fundamental to the problem that we're discussing. Different people vary in their appearance, but each person also varies in their appearance. Separating those two sources of variability to understand what you're looking at is computationally difficult.