Hand quilting thread should not be used in a machine; it can gum up the tension badly and require a service call. The thread is coated to make it stronger and more tangle-proof for hand quilting. I think the "dual-purpose" refers to the cotton in combination with polyester.
Just about any thread can be used in a sewing machine *except* hand quilting thread!
I should add that you certainly can use cotton-covered polyester thread in a machine as long as it is not labeled hand quilting thread.
I think the standard Coats & Clark's "dual duty" is machine sewing thread that can also be used for hand sewing; it would not be labeled hand quilting thread, though.