Aspects of the present disclosure include a connector that is suitable for connecting medical suction tubing with at least two different types of fluid ports of a medical fluid collection system. In certain aspects, the connector includes a generally cylindrical body portion having a cylindrical outer surface extending generally parallel to a central longitudinal axis of the body portion, and an inner surface defining a primary conduit extending through the connector. At least one lateral closure wall extends radially outward from the outer surface of the body portion. At least one annular skirt wall extends longitudinally from the at least one lateral closure wall, including a first annular skirt wall that serves to receive an open mouth of a first fluid port having a relatively small diameter, and a second annular skirt wall that serves to receive an open mouth of a second fluid port having a relatively larger diameter.