Can you take pics all with the same lighting. Some look taupe and some look red . If those are the actul colors in different spaces IMo it would not matter what they are they would be rip out for me.

It appears these photos are from somewhere in Europe.

I'd guess these are some variety of Quarry Tiles.

These are also made in the USA but colors and sizes will be different.

https://www.pavestone.co.uk/inspiration/interior-flooring/

The photos are from two unrelated homes in Palm Beach and Montecito, that I unfortunately have no access to :(.

I wasn't aware of quarry tiles previously. I'll have to look into those.

Why do you want to know?

Look like brick and quarry tile in the first photo. Might be slate tile in the second photo.

I'm guessing the herringbone is brick. I have seen where it was originally a patio which was subsequently incorporated into the house. This is probably more common in the South, where winter heating is less of an issue.