Polished: This is the mirror-gloss you are most likely familiar with and is low maintenance. Soapstone will not take a full polish.
Honed: This is smooth to the touch, like polished, but lacks the shine. Honing makes it more susceptible to staining. Water and oils will eventually dissipate out of granite but it will show fingerprints and rings of glasses more then the polished. Soapstone is always honed. .
Brushed, Antiqued, Leathered All of these terms are interchangeable. They signify a rumpley feel and moderate shine without gloss. The size of the texture depend on the size of the crystals in the given stone. This finish is also susceptible to staining as you have taken a layer of protection off.
Flamed This is a rough, sand-paper like finish more suited for exterior applications, but works great inside on vertical surfaces like fireplace surrounds.
Edge Profiles:
Verde Borgogna Brushed Granite