In addition to what @
Rainbeetle said, while I can't comment on those specific sites, I play three other sites with 'custom' options.
Two of those, Gryffs and Khimeros, have no way to get 'gen1' pets without the custom maker. (Gryffs, to be fair, has contests where the owner of the site creates the custom and send it to you). Like the two mentioned, they have a variety of markings, and there are layering and fades, and being able to 'add' markings to a lineage by breeding pets etc.. Gryffs, at least, also only allows you 12 markings on a custom gryff, and you have to pay for each one (not sure about Khimeros, it may allow a pet with all markings but you have to pay for each one). This keeps the breeding aspect of the site, because if you want more markings you have to breed them onto the pet.
I don't know that much about Khimeros, because I am not that really into it, but I think it is a lot like Gryffs (believe it was started by the same people, though they are owned by different people now, but I am not really sure).
The other site that allows 'custom' pets is Sylestia.
However, their custom generators are VERY limited compared to other sites. They also have ways to obtain other gen1 pets other than the custom.
On Sylestia, you can obtain or buy 'essences' that will allow you to pick (if I remember), lowest level, 1 trait, and higher two 2 traits, out of six possible traits. (I may be 2 and 3 traits, but not sure), and all colors, though colors can be different on the 'created' pet, with, again, the lowest essence being the least accurate, and the highest essence being the most accurate.
They also have ways to 'capture' wild pets, which are gen1s, though those are often not worth anything, due to having something called 'themes' that are pets with specific color patterns and 'tag' that gives the name of the theme. You can also catch these in some places, and at certain times for some, and you can also create them, though not with essences, but rather with other mechanics that are associated with festivals (it seems complicated trying to explain it, but it honestly isn't all that complicated). Again, created pets can have up to 3 traits, though it is hard to get the item to give them three traits, and wild caught pets can have up to 5? Maybe they can have all 6 traits filled, though the chance of finding one of those is next to non-existent.
To complicate things, they also have a vastly different breeding system that works more on a punnet square system, with hidden and carried traits, as well as visible traits. (and the pets that can be caught have trait points and it takes two trait points in one slot to make a visible trait in that slot, which is why I can't remember how many visibles a wild caught pet can actually have. I know they can have a carried trait in each slot, but not sure about visible traits in each slot).
They also, unlike Gryffs and FR, have different 'species' of pets, and unlike Khimeros, these pets cannot breed together (Khimeros has the ability to create hybrids, by breeding two different species of pet together).
Basically, the tl;dr is that these sites with custom makers have vastly different systems of breeding, and they are usually MUCH more complicated. They also don't tend to have ways to obtain gen1 pets outside of the custom makers.