It might be limestone.

Thanks but it seems like some sort of metal? It is very smooth. There are large square "tiles" that are screwed place. The bottom photo shows it next to the bamboo floor in the dining area. By the front door where there is a lot of foot traffic, it is the lighter brown color in the photo. Not sure how to clean it or care for it. It is in a house my daughter's family is renting and the whole place has an industrial chic feel.

The way you asked the question, I thought you admired the flooring, and wanted to know what it is. Who cares what material it is? Your daughter (not you) ought to ask her landlord in an email which products to use on the metal floor.

Seems absurd to put metal on the floor. Perhaps buy her a large rug as a housewarming gift.

If you are curious, unscrew a piece and see the back and profile edge, as long as it's not T&G. My guess with the purposeful color fade would be some sort of masonite product or vinyl laminate. Just Swiffer overall and shop vacuum the gaps and screw heads, I would stay away from liquids with those same gaps and screwheads (even if S.S. screws).