White markings put themselves over the pony's body color. This include pinto markings, face markings, and leg markings.
The very specific placement and shape of markings isn't genetic. Randomness is a major factor in pinto and regular white markings. A foal having a similar looking blaze, star, sock, etc to a stallion should not be used as proof of parentage. Full siblings often look very different from each other. Clones have different markings from their source and also from other clones from the same source. Ponies can have the same or similar color genetic makeup with very similar white marking, but only be slightly related or not at all.
White suppressors reduce the amount of white markings a pony has. The pony has white markings or pinto white markings and the amount of white is reduced by a suppressor. The white markings or pinto pattern is trying to put white on the pony and the suppressor is working to stop it. Occluding spots and cryptic are two white suppressors. Black/bay has long been known to suppress white markings. In general black or bay based ponies will be less flashy than chestnut based ponies.
White boosters can increase the amount of white markings a pony has. A pony will have white markings or pinto markings and a booster will cause the pony to have more white. Chestnut or chestnut based ponies will, in general, tend to be flashier than bay/black based ponies. Having more than one pinto pattern can be a white booster. In Chincoteagues the ponies that have both tobiano and splashed white often have more white then if they just had one of them. There are several white boosters, with likely more to be found, where that's mostly what they do. Alone they don't result in much white, but when combined with another then adds a lot more white. White boosters of this type that Chincoteague Ponies has been tested to have is White 20, White 34, and White 35. When a pony has a white bootster and another pinto pattern the amount of white produced by the other pinto pattern will sometimes be increased.
White markings are minimally affected by the foal coat. White markings will get smaller in size and slightly shift in placement as the pony ages. The shape itself won't change.