The whole reason various populations look different is that they have different genes along with different average frequencies for (nearly identical) genes driving their phenotypic appearance.
Migration patterns have separated populations, and then evolution acts on the genes of the descendants to alter those genes. New genes then achieve variable degrees of penetration in the descendant groups. There are other reasons gene pool average frequencies might be different even where (nearly) similar genes retain an essentially unaltered function.
Let me give a few examples.
For a gene variant:
MCPH1 Haplogroup D variant is about 70% penetrated into Eurasian poplutions; we hardly find this variant at all in groups whose recent ancestry is sub-saharan africa.
For genes with similar function but different average frequencies, driving differences at a SIRE group level:
HbS is found in much greater frequency within populations where malaria has (historically) been endemic. It’s thought that heterozygosity for S has some protection against malaria. If you look at black and white SIRE groups in the US, you won’t find the same average gene frequency for HbS, and therefore even at a self-identified level of grouping, there will be a different outcome for those two groups if you look for SS-based sickle disease (or, for that matter, the average ability to survive malaria).
For physiology:
Any number of genes driving physiology are thought to be found in average frequencies which differ among SIRE groups. Reference ranges for creatine kinase are different for adult male blacks and whites, for example. If we look at ACTN3, the variant with the rs1815739; R577X mutation has a much higher frequency in asian populations than african ones.
The examples of gene variants which cluster by SIRE group would fill a book, and more are being identified every day.
It is this average difference in genetic pools that drives so many of the outcomes we see among even self-identified groups. I may be Navin Johnson, but if I self-identify as “black,” then I have self-identified with a group that has a higher average outcome for HbS sickle cell anemia, and a lower average outcome for cystic fibrosis even though I myself have exactly the opposite chance of having that outcome. This is because the average gene pools of SIRE groups are quite different, and quite easily shown to cluster (because not only are genes and gene frequencies different; penetration for new genes is quite different).
Many people (and I believe you were one of them, at least in the past), get confused because we use the same name (nicknames, really) for parts of the DNA code lumped into a “gene.” However, just because a “gene” has the same nickname does not mean it’s an identical gene. As a nice example, there is a gene nicknamed HGMA2 that has been linked to brain size and intelligence. People with one of its variants (with a single substitution of a cytosine for a thymine at a single position), have an average of 2% larger brains and perhaps a 2% increase in intelligence. A beginner to the world of genes might think, “Well; we all have HGMA2, so we all have the same genes, right?” The answer, of course, is that we all have (about) the same general genes (humans are pretty much humans), but the are definitely NOT the same genes from human to human. Evolution is constantly at work altering them all, and when she’s lucky enough to create a variant that produces a reproduction advantage, the descendants of that person gain that advantage.