A dishrag is a cloth for washing or wiping dishes — what many books call a dishcloth. Dishrag is informal American: rag already hints at a cloth that is not fancy, maybe old, wet, and a bit sad. You wring it out, wipe a plate, hang it over the tap. British English prefers dishcloth or washing-up cloth; dishrag can sound rough to British ears. People also stretch it: limp as a dishrag means weak, tired, with no strength left, like a wet cloth that cannot stand up. That picture is more common in speech than in careful writing. It is not a towel for drying your hands, and it is not a sponge, though some families use the words loosely for whatever lives by the sink.