Warren in Lancaster, PA
Older texts have two types of water stones: rub stones and rag stones. The rub stones were coarser and may be thought of as flat grindstones. There was some overlap in function between the grinding wheel and rub stone. I think they tended to be sandstone like the grinding wheels. Nicholson mentions grinding stone (wheel), rub stone and oil stone. Here is a large coarse stone from Roubo:

Rag stones tend to be schisty stones or fine sandstones, maybe the kind of thing one might use as an all around stone, for knives or axes or as a set up for an oil stone. Rag stone can also refer to a type of building stone.

In 18th century English, fine stones are often called slates or honing slates. Not that necessarily they have anything to do with the slate we put on a roof.

Holtzapffel reprints (from a journal article) a list of stones available in England in the late 18th century. Here are some: