Off the top of my head (Score 1)

The telomeres (that is, the ends of chromosomes) are shortened a little bit each time the chromosome is copied (the DNA replication process doesn't work very well when the strand suddenly comes to an end, so it kind of hacked a solution together). Clones will inherit the telomeres of their donor, while the telomeres of twins have no such relationship.

There is some evidence, though not conclusive, that telomeres may be linked to aging.