The difference between polished and tumbled tile is the texture. Tumbled tile is designed to have a dull, worn texture, while polished tiles are smooth and shiny.
Brick Light Travertine 3x6 Tumbled Tile

Choosing between polished and tumbled tile for your home is a matter of preference. Tumbled tile gives spaces the distressed or antiqued look that's popular now, while polished tile is more classically traditional.
Ghibli Granite 1 cm Polished Tile

Here is an example of a tumbled tile kitchen backsplash:

And here is an example of a polished stone backsplash:
