In cell division, are daughter cells identical? I understand that after a cell replicates, there will be two daughter cells instead of one. But wouldn't one of them be the old cell that created the second one? The old cell having gone through G0, interphase, and mitosis and after dividing wouldn't it be somewhat different from the new cell (the old cell's telomeres having shortened, having already undergone the cell cycle and so on)?

Here is a picture to expand on my comment better. From wikipedia:

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In the above diagram, the red chromosome represents one homolog while the blue chromosome represents the other homolog in the pair. After replication in Interphase, you have two homologs, each consisting of duplicated sister chromatids. You can see how we have the one enlarged cell in Mitosis be cleaved into two daughter(diploid) cells.