I've always gone with whichever version of background better fits the current game I'm running, and if neither one is strongly indicated I'm fine with any sort of mix of the two.
To wit, there can be both groups of true-breeding Tieflings of common appearance and lone individuals whose heritage has manifested in different ways.
A player basically gets to decide on their appearance and background, although I generally add the basic caveat that Tiefling (or Aasimar/Genasi/whatever, but especially Tiefling) heritage tends to breed true and dominant - the more Tiefling blood you have, the more altered your appearance is (exceptions existing, of course), and it can't really be bred out of the bloodline at all.
For example, if two non-Tieflings (or Aasimar/Genasi/whatever) with even a hint of plane-touched heritage were to breed, their child would have more plane-touched heritage in them than either one of the parents, and if that child was a PC could choose to use the stats for the appropriate plane-touched race rather than human if they wanted. If that child then later bred with another plane-touched, or even someone with a hint of plane-touched heritage, the resulting grandchild would generally end up using the game stats for the appropriate plane-touched race (unless they were also a PC and chose to use the human stats because it fit their narrative backstory better)...