If I do a detail then I tend to use the Lambswool/Sheepskin mitt though I do think if its from the same type of animal so why name it differently?. It feels better, fluffier almost and tends to hold water which helps in cleaning. For general cleaning I will use a Megs wash mitt. This seems to like grime and general crud. I've have had it over 2 years now and is washable, a low wash in the machine without softener brings it up like brand new.
With my old car I used a sponge from a kit that you can get from a local car accessory supplier which did create swirl marks on the paint. I've noted that with a sponge compared to a wash mitt; the wash mitt tends to clean better and gets into places that the sponge does not. The better quality mitt I have used does tend to clean better (this is using a dual bucket method with warm (car shampoo) to cold (clean) water)
A basic answer to you question,
General purpose (bodywork>trim>rims) Megs Microfibre Mitt (or alternative)
Bodywork only > Lambswool/Sheepskin
Buffing or Polishing > Microfibre Towels,don't bother with a mitt for this