In many cases, there may be no practical effect. However, laws like the Wilderness Act do allow certain activities in designated wilderness which may be incompatible on a wild and scenic river, e.g., water resource developments if authorized by the President. In addition, wild and scenic river designation prohibits federal participation in, or assistance to, water resource developments upstream or downstream of a designated river (potentially outside the wilderness area) which may adversely affect the designated river segment. Agencies are required by policy and law to evaluate potential additions to the National Wild & Scenic Rivers System located in wilderness.
Source
Interagency Wild & Scenic Rivers Council