Ceramic and porcelain are the same thing. Porcelain is just a particular kind of clay (other kinds include stoneware, like sturdy dishes and terra cotta like flower pots). Some ceramic tile is porcelain and some is more like stoneware. The bathroom tiles tend to be very smooth and other ceramic tiles (which I use exclusively) are rougher and provide better traction. Slate is stone and is heavier. It can be hard to get slate that's regularly sized. People do use it but be aware that it's a lot heavier.
Aliza