People should do what they are comfortable with. In the shower, I don't use a washcloth for the rest of my body, so that's not an issue for me. When I used to sometimes wash at the sink instead of taking a shower, I did have a separate washcloth for the rest of my body.

I didn't feel a need to launder them separately, as they were both washed out with water after using them, and the laundry itself should get them both completely clean. But what gets separated doing laundry is a whole 'nother topic.