Most floors we see are garage slabs, shop floors, or concrete that's been under carpet, tile or an old coating for years. Polishing doesn't cover the slab with anything new. It works with the concrete you already have, so the slab's own mix, cracks and patches become part of the finished floor. That's why I'd rather show you what's going on with your slab before you pick a finish.
The price mostly comes down to the room's size and what's sitting on the slab now. Carpet glue, tile mortar or an old coating has to be stripped first, and cracks and holes need filling. Each step toward more exposed stone or more shine adds grinding passes. The schedule turns on the same things, plus when the room can be cleared, and your estimate gives you the figure for your floor.