All the early American breeds, particularly the stock horser breeds, started with more "open" registries and shared a fair amount of ancestry. In several early pre-registry programs and ranch programs, they had horses of all colors and patterns and kept and bred those with ability regardless of color. When the registries formed, those of the appropriate color went into those registries-- they might have been full siblings, but the app colored ones went to ApHC, and the solids went to AQHA (and a bit later the pintos went to the Paint horse registry).
Horses with Appaloosa genetics can express Appaloosa traits very minimally (for example, being born solid with some mottled skin and striped hooves, may or may not roan later).
There are several documented Appaloosa colored horses back in the 40's and 50's and even into the 60's that started out solid, were registered AQHA, but later colored up enough that AQHA pulled their papers and they went to ApHC. Some of these even had AQHA offspring before they were obviously app colored, which remained registered. There are also some Appaloosa colored mares known to have been used in early Quarter Horse breeding programs that never had their AQHA papers pulled because their owners "kept them home" and didn't show them to anyone after they colored up, but quietly kept using them as broodmares.
In 2004, the AQHA rescinded their rule against registering horses with "misplaced white" markings and they now will register any "number to number" Quarter Horse no matter what color/pattern it is born with or develops. This was done mainly to keep the paint cropouts in the registry, which AQHA had been losing to APHA for many decades, but a few Appaloosa-colored examples are starting to show up now too, now that they can be AQHA registered and are not being hidden, disposed of, or sold off as grades.