There are likely to be genetic differences, but ones that were present at the time the groups split.
Who had access to the bunkers? I'm sure it was not random luck.
The other differences will be that people with a variety of disabilities and health conditions (which may or may not be genetic) are more likely to die off if they are in the wasteland. Since most such conditions are genetic only in terms of how likely you are to get the condition, this will probably not affect the actual genetics. Yet.
For example, there aren't going to be a lot of wastelanders with conditions that affect their stamina (running away from danger), eyesight, or mobility, for example, a heart condition that shows up under physical stress. But the genetics involve multiple alleles throughout the genome (not a single inherited SNP) so it is way too early for this "natural selection" to change the gene pool in any significant way.
Though even one generation can change epigenetics. Methylation markers on the DNA itself that turns certain alleles on or off. Epigenetics can carry information acquired after birth and pass it along to the next (unborn) generation. It does not change the actual DNA but markers are inherited to a degree. Something like famine can affect generations that never experienced it.