Certain men have very strong genetic traits that persevere for centuries. While I have no idea what Robert “King” Carter or his second wife Elizabeth Landon looked like going on 400 years ago, I do know that my late grandmother’s attorney was a dead ringer for Jimmy Carter, but with red hair. He was her 2nd cousin, and mine twice removed. So resemblance among male descendants of an old and prominent family does not necessarily mean that any of them share immediate paternity. It could go back quite a ways.
Did you see the pic on this thread of the femal Jefferson descendent?