Just a little ceramic information to share as a potter. Vitrified simply means the clay has become glass like by being fired to its proper maturing temperature. Usually ceramic tile means it is a lower temperature clay like earthenware or terra cotta. Porcelain is fired to the highest temperature and is more vitrified if you will. This usually means it is less porous to to absorb water and harder. Low fired ceramics with glazes much darker or lighter than the clay body will show chips easier. Rectified has to do with making the edges precise enough to fit smoothly together for less grout lines. So porcelain cost more to produce but it is more sturdy. All clay tiles should be vitrified.

I think that is more about what you like, concrete usually denotes a more modern feel, almost industrial if that is your style do concrete if not find a tile you love and do that.

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@Rock Doc: Are you addressing this to me? I haven't actually bought these tiles yet - when I do, I will definitely be going for the handmade ones. They're a work of art and irreplaceable in my opinion. However, there are also screen-printed tiles available in the market in more or less the same patterns; the workmanship is of course different, but you get them cheaper, and they're also more easily available. You could give that a shot. I'd recommend Aakaar Flooring Solutions - they're here on Houzz and are able to provide both the above-mentioned types.