Basements in both those states.

I’ve heard people in Oklahoma say that basements can’t be built because the soil has too much clay, yet I’ve seen them in older homes there.

I’m starting to think that “basements can’t be built in X state” is some kind of pervasive urban myth.

I mean, don't get me wrong, you can build a basement anywhere. Its not like the ground is truly impermeable. Its really just a question of if its worth the maintenance or not depending on the terrain around. If you're going to have your sump pump constantly run because your basement is below the water line, you're going to have a bad time. If you've got expansive soils that'll constantly be changing the direction of load on your basement walls, you're going to have a bad time. Coupled with the fact you don't need to dig that deep to get deeper than the frost line, its usually just really not worth it. So its not that they can't be built, they just can't be built economically.

Really wealthy people in Texas might have a basement; its not impossible! Some really old homes before slab-style construction might have basements as well. Or they might be living in the high deserts out in West Texas. But like easily 99.9% of homes built in the majority of Texas do not have basements. If I were to ask everyone I know if they knew anyone who had a basement at any time in any home they ever lived in, the answer would probably be "no" almost every time. Finding a home built since the 1940's in this area that's less than $10M with a basement is practically finding a unicorn. Except its an expensive unicorn needing constant maintenance.