You can find that SAME exact floor (along with many more finishes of that same pattern) from the company called ARTO Brick located in Gardena, California. You will NOT be disappointed with their selection. They are the manufacturer of these same types of tiles. They will even do custom tiles for you!

The floor tile is from Classic Tile and Mosaic:http://www.classictileandmosaic.com/Catalog/OC_Terracotta_Tiles.pdf

Can you stain an existing red Spanish tile to achieve this same white washed look? or do you need to buy the tile already white-washed? thanks!

Yes, you can use a white-wash saltillo stain.

What do you call this white-washed floor style?

Here is a link to this Artillo style tile: http://www.arto.com/series/Artillo?keywords=2c I am not sure how they sealed the tile so I can't answer the "white-washed" part of your question. Hope this helps. ^Lori

Thank you!