Adam Clarke on Acts 19:12

Handkerchiefs or aprons - Σουδαρια η σιμικινθια, Probably the sudaria were a sort of handkerchiefs, which, in travelling, were always carried in the hand, for the convenience of wiping the face; and the simikinthia were either the sashes or girdles that went about the loins. These, borrowed from the apostle, and applied to the bodies of the diseased, became the means, in the hand of God, of their restoration to health.

The diseases departed from them, and the evil spirits went out of them - Here, there is a most evident distinction made between the diseases and the evil spirits: hence they were not one and the same thing.