When I just looked using "what is" this is what I found. "Rectified tiles are ceramic or porcelain tiles that have been precisely ground and machined to give them near-perfect straight edges and exact dimensions. These tiles provide a very clean, symmetrical look, and allow for extremely fine grout lines of 3mm or less (typically using unsanded grout,."

I would ask for another quote if the first one did not explain the difference and just gave you a name and price.

Porcelain is better for high traffic areas than ceramic. A porcelain tile can be rectified tile, so it's weird they're presenting it as two opposing types of tile. Check to make sure the tile is "color through", especially for area where it might get damaged by traffic or items being dropped (i.e. a kitchen).

Thank you for comment. I am putting hardwood on my kitchen