Grind and seal
This is the more affordable option and it is what a lot of people picture when they say polished concrete. The floor is ground back a little to open up the surface and even it out, then a topical sealer is rolled or sprayed on to give the sheen and protect it. The look ranges from matte to gloss depending on the sealer, and because it is only a light grind you can choose how much of the stone in the slab shows through, from almost none to a light salt-and-pepper.
Grind and seal goes well over an existing slab in a renovation, and it is quicker and less disruptive than a full polish. The trade-off is the sealer sits on top of the concrete, so it wears at the surface over time and gets refreshed down the track, particularly in high-traffic paths through the house.