Whether used on a table or (as with a picnic) on the ground, a 'tablecloth' is a 'tablecloth' = what goes on some bare surface and the plates are put upon prior to eating.
The difference here is: one is to be washed and used again. The kind you are referring to is a 'disposable tablecloth': 'tablecloth (meaning made out of woven cotton) whereas 'disposable tablecloth' refers to one often made of paper. (They may make them out of some other plastic-like material, but the point is, they are not intended for long-term use, and not regarded as valuable.)
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