You could say that a dry run is a type of rehearsal. Specifically, the type of rehearsal where you run through a show without stopping to actually work on issues, for the sake of testing where the ensemble's cohesiveness and preparedness is.
Rehearsal is a time set aside to rehearse, or, to work on a specific set of pieces, a show, or some other event. Sometimes, a rehearsal is involved in the sense of working on issues with the group, and addressing questions and concerns. On the opposite is a very hands-off type of rehearsal, which is the dry run. This is the rehearsal that can happen at specific determined checkpoints, to make sure that things are ready, or to assess all the issues at once before settling on a plan to address them in full before performance time.