I would like to add that when attachments are used in crown and bridge, rigid attachments tend to transmit forces down the long axis of the abutment crown. They also tend to have greater retentive forces. Resilient attachments, which for C&B are all extracoronal as well, are intended to transmit the forces to the edentulous ridge and avoid possibly overloading the abutment. When two attchment RPD's oppose one another, the attachment should NOT be the same type, and the rigid USUALLY go on the maxillary.
In terms of implant overdentures, a rigid system is used with bars as the mechanics are IMPLANT SUPPORTED.
When the attachments are stud type or rotating, like a Hader bar, they are classified as TISSUE SUPPORTED and IMPLANT RETAINED.
so ti comes down to what is taking the forces, the implant (rigid),or the tissues/ridges (resilient). Keep in mind that using an ERA or Locator on a milled bar with overcasting renders it a rigid type.
Hope that helps.