If you wipe the table with the same cloth you use to wash dishes—and this is usually a small square—I would say “dish cloth.” The connotations of wiping a table with a dish cloth would be that the fabric was wet. (I do this). If you wipe the table with a piece of cloth that used to be clothing or some other article or even something sold for the purpose of cleaning—and this is usually slightly larger—I would say “rag.” The connotations of wiping a table with a rag would be that the fabric was dry. Of course, when I wash the dishes or the table, I often use the washcloths that came with sets of towels (On myself, I use those round net things or brushes in the shower). Is it still a washcloth if I use it for the dishes?
In AE the closest thing I can come up with is dustcloth. Of course you'd need something else if by "wipe" you mean any chore involving water.
Wet wiping is mostly done with sponges, I'd say, or a wet washcloth or dishrag. You know, since a rag is a cloth that was once used for something else, a dishcloth that gets a little too stained or greasy or threadbare-- could get demoted to a dishrag. Fit for wetting, wringing out a bit, and wiping down tables and countertops, which don't need to be clean enough to eat off of.
Following the natural succession, a dishrag that was too funky or tore-up to wipe a table with would be perfect to use on the stovetops, or wiping up spills on the floor.