Yes there is difference and it originates from the fact that since the chromosomes live in the nucleus of a cell and if the DNA differs, then technically so should the cell. Although, If we break down the compounds and proteins to elemental levels, then they have the same composition.
A Gene of an Indian person would differ from that of an African person and this would result in the cells being different........ but there is a big 'BUT' coming......This difference is much more closer to a difference that two different Indians would have amongst themselves.
Thus, the cell of a person of one race would differ from the person of another race, as it would differ from his own race.
As an example: One race may have a similar shape of skull than the other race. This means that a genetic difference exist. But the thing is that two people of the same race may actually have even a wider difference between them, than they have from a different race.
Since the genes are what form the basis of our biological make-up, therefore different genes mean different cells - even if you are from the same race.
Yes, your cells contain DNA and that is what makes us all who we are. Now a scientist could go in and introduce protiens at certain times and change the DNA of that cell and could quite possible change a persons race if enough studies were done. We do not expierament on humans so we will most likely not know the answer to that possibility for quite some time.