Nylon bag vs plastic bag

Solution 1:

No, they can't be used interchangeably (in the US) since nylon bags and plastic store-purchase-type bags are different materials entirely.

Nylon bag (typically called a laundry bag)

Plastic shopping bag

Edit: and to Aml's point, nylon is a synthetic woven fiber and plastic is not.

Solution 2:

Yes, Nylon is a plastic, but the lightweight plastic bags they give you at stores are not nylon. Nylon works well as a fiber, so a 'nylon' bag could refer to a woven bag, such as are re-used instead of re-cycled. {And I don't think it was construed as requesting a bag for nylon stockings.}