Floor tile
 

Is the Spanish word teja, or does that usually refer to roof tiles?

A teja is indeed a roof tile. For floor tiles you probably want baldosa. For walls, azulejo.

I don't have any mnemonics for the second or third, but for the link between techos and tejas I just have to think about the Les Luthiers scene where Rabinovich and Mundstock ask for the carta in the restaurant (at 10:14; the timestamp doesn't seem to be supported by the automatically added VIDEO tag):

I agree with Pjt. In Mexico we also say "loza", "loseta" or just "piso". :)

Oh. Now I'm thinking baldosas are more likely to be very durable like stone flooring and lozas are thinner perhaps made of vinyl.

"Loza" can never be vinyl, linoleum or any synthetic material. It's some sort of clay; that's why it's also the same name for the tableware. :)
And although "loseta" is not a material, but a close synonym to baldosa. We use that for smaller or slender clay tiles.

Synthetic materials are usually "piso". Personally, I have never heard "baldosa de linóleo", but Google says it's not so uncommon. :D

- Para instalar el piso de linóleo, contrate a un profesional.
- No pases por ahí, las lozas están mojadas.
- Quiero ponerle piso de loseta a la cochera.
- El patio tiene unas baldosas de concreto muy resistentes.

Wall tiles are azulejos in Spain. HTH

In the back of my head I always thought that azulejos were blue and white tiles, but they can be any color I guess.

In Mexico "azulejos" can be any color, but they're rather thin, often smaller than floor tiles, and shiny. :D