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A mop has a stick part.

I don't know the term for a piece of clothes without stick, for cleaning something held by hand.

What should I call a piece of towel or a similar thing that is used to clean floor/window/shoes?

In my language, there are two related terms: one is for wiping a quite dirty thing, the other is for wiping a rather clean thing.

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2 Answers 2

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I think you are looking for Cleaning cloth:

a cloth used for cleaning; specifically, a cotton fabric of coarse spongy texture.

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from Amazon

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You could call it a rag if you're using an old piece of cloth (could also be an old towel):

: A rag is a piece of old cloth which you can use to clean or wipe things.

(Collins Dictionary)

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