We might look on aging as damage that happens as a stochastic, inevitable consequence of the operation of a biochemical system. So the buildup of chemical gunk between your cells is a part of aging, while those times you managed to break bones in your enthusiasm for life are not aging, despite the fact that what's left in the wake of those unfortunate accidents is definitely damage.
There are always special cases and grey areas worth thinking about, however. Such as teeth, for example, as I was reminded earlier today. Teeth have a pretty hard time of it, actually, when you stop to think about it. Even in this modern age our teeth maintenance technologies remain woefully inadequate in the face of bacterial species that break down enamel, and so our teeth are one of the most failure-prone and damage-prone parts of the body - and they get to the point of painful dysfunction far earlier than the rest of our organs if left to their own devices.
But that isn't aging - it's parasitism, no more aging than the consequences of contracting malaria. It's still something we need to fix, of course, and I post on this and related topics because it is of general interest to anyone who follows research into rejuvenation and regeneration. If most or all of us suffer a particular form of bacterial malfeasance that manages to be as damaging as that which chews upon our teeth, than dealing with that problem has to be included in any general toolkit for enhanced human longevity.
As an aside, I should note that the hard components of teeth do age:
enamel thickness related to age showed a steady decrease, beginning at approximately age 50.
There are apparently chemical composition changes, increased brittleness, and so forth - none of which seems to have much to do with the bacteria that cause cavities.
Another completely unrelated grey area is something I touch on frequently: the structural changes that take place in the due to exposure to infectious agents. The adaptive component of the immune system performs throughout life just as it evolved to do - which means it devotes space and cells to remembering the pathogens it has encountered so that it can effectively destroy them in the future. But by continuing to function in this way, it becomes less and less effective over time: in later life too much of its capacity is taken up with memory cells and too little with killer cells. So quite aside from what we might think of as biological aging, the adaptive immune system succeeds itself into an increasingly broken state just by doing its job. Whether or not we call this process aging, it still has to be fixed, auch as by using targeted cell destruction therapies to eliminate memory cells and free up space.
There are other examples. But you get the point: not all of the degenerations that we suffer with advancing age are in fact aging per se, or at least they will not fit into the usefully narrow definitions of aging that I find helpful. They will still need to be addressed, prevented, and their consequences repaired.