Really? Any specifics?
Sure, here's one example. It would be nice to know where in the genome selective sweeps have taken place in recent human evolution. A selective sweep occurs when a variant undergoes positive selection (i.e. is favorable compared to other variants) and therefore becomes much more common in the population, bringing along with it its immediate chromosomal neighborhood. Selective sweeps within the last few hundred thousand years should leave traces behind in the genetic variation in their area; very recent ones -- the sweep that brought lactose tolerance to high frequency in parts of Europe, for example -- are easy to spot. One test for such a trace of positive selection is the presence of an unusually large number of high frequency derived alleles at neutral sites. Derived alleles (that is, the variant that arose recently due to mutation) are usually at lower frequency, and a statistically significant number of high frequency ones in a region is evidence for selection. You can't tell just by looking at position, however, which allele is derived and which is the original -- you can only tell by looking at the sequence for a closely related outgroup, usually chimpanzee for humans. Thus the actual test is to look for a variant site at which the allele that's different from the chimp allele is at high frequency. This assumes, of course, that the site started out having the same allele in chimps and humans, which is obviously the case if humans and chimps share a common ancestor.
There's another example here:
No webpage found at provided URL: http://www.broad.mit.edu/personal/sfs/correlation.pdfKey to the analysis is the assumption that humans and other primates share a common ancestor. There are plenty of other examples. (Surprisingly enough, I do actually have some idea of what I do for a living.)
Would it matter if the aforementioned organisms were related via Common Creator or due to a design or does it matter only if they shared a common ancestor?
I don't know. I haven't been able to find anyone who can tell me what predictions the hypothesis of a common creator makes about genetic similarities and differences. Common descent makes quite specific predictions, and is therefore useful. Can you give me any predictions based on your hypothesis?