Many of my pieces are unglazed on the outside. I fire all functional ware to at least 2165° F (cone 6), which shrinks the particles of clay close together and makes a stain resistant surface. For instance, lipstick will come off of a mug, even if the outside isn’t glazed. However, staining is still possible if you aren’t careful! To prevent permanent staining, please hand wash the same day you use your item. To get out stubborn marks, I recommend buffing the affected area with baking soda and a little water.
Glazed items are dishwasher safe, but I recommend hand washing. Generally speaking, clay will absorb small amounts of water if it is soaking and this may weaken the piece over time (imagine a river eating away at a stone mountain). Giving a piece a thorough wipe-down and letting it air dry will help it last for years to come.