They are two different ideas. "to polish" means to rub something in order to make it smooth and shiny. For example, you polish the silverware (silver or silver-plated forks, spoons, knives) in order to make the shine. If you "polish" a floor, you are trying to make it look smooth and shiny.
"to mop" means to wash or to clean. And when you're speaking of a floor, you actually use an implement called "a mop" to do it. A mop has a long handle like a broom, but on the end there is a soft material, which is usually absorbent. If you "mop" a floor, you are trying to wash or clean it. The verb "mop" itself does not emphasize making the floor look smooth and shiny.