Over here, most definitely NOT
Sabino is in most horse breeds- TB Arab etc and it is responsible for "normal" white markings on all horses and ponies with a few exceptions (Icelandic do not have Sabino, I believe, Lewella and I disagree on whether or not Native Shetlands have Sabino
) It is definitely a gene- a many faceted gene, that occurs in different ways in different horses and generations of horse. From the same breeding I have had:- TB type Bay with minimal markings, Splashy - flashy Palomino with high white, Full Sabino with belly splash , white over knee, bald face, spots in jowl, the whole nine yards!! This was from two Sabinos. Unless encouraged to express it usually stays fairly minimal, when added to another pattern, especially Splash or Frame, it tends to go potty!
It is no more related to the Overo pattern (ie Frame) than is Tobiano- all three patterns ( Splash, Frame and Sabino) that are lumped together as "Overo" are quite separate genetically and no closer linked to each other than is Tobiano!! I have seen Appaloosa- the breed not the pattern- with white socks
not described as Pintaloosa- in fact the person went potty when this was pointed out. Apparently the Appaloosa Society does not "count" leg/face white- this may be the cause of the apparent link with Pinto patterns in some Appy patterns. Over here no white markings or Pinto breeding is allowed.