Yes; different aging process. Aging can be thought of as being brought closer to death. These skills begin to lack efficiency and have accumulated mutations.
Age is a function of time. It is not a disease process, although, the aging process comes with phenotypic changes in the organism. It will be difficult to identify original parent cell, except specific genomic markers have been typed and recorded.
In the strict sense of wear and tear, the age of a single celled organism relative to the population can actually be determined by typing the nucleic material, and mapping it against a random sample of other cells in the same population. The presence or absence of stop or delete codons may be used for example.
But it's helpful to understand that aging is a function of time.....the wear and tear aspect is just a side effect.....