It is just a max expression of the paint gene be it Tobiono or Overo. Just like some of Gunners foals are ALL white not a speck of color anywhere. If you DNA test them they come back Bay Sorrel black and so on yet they are all white.
By "white foal" are you meaning the one in the photo with the mare, or one who is pretty much totally white?
If the one with the mare, I would not consider that a white horse. Pinto with more white than color, yes. But not white.
If you mean a "solid" white horse, could be Dominant White (but I would say not in this case, the parents don't look to be DW), could be maximum sabino (SB1SB1), could be a loud homozygous splash, or just a combo of white genes (sabino, splash, tobiano, frame).
He's not white, he just HAS lots of white. It's just how his expression of color came out. My Paint filly is the exact same - almost identical in fact with a black head and two black flank spots on a white body. Both her parents were dominately black with "white patches" as your boy's parents are.
Heck, you could have two solid horses produce a horse that looked like your boy if they were only minimally expressing their own copy of the gene.
As others have mentioned, genetic-wise, the foal is colored, but most of the color is masked by the pattern, resulting in being mostly white. It's actually very common in toveros.
Here's ours..left side all white on the body, right side with her chestnut color.