Back in the very old days (late 1800's/early 1900's maybe?) Baylor University had a medical school. The faculty got upset about something and moved to Dallas, where they started Baylor Hospital (now BUMC). Then in the 1940's-ish, some kind of falling out happened again, so part of the faculty left Dallas and moved to the new Texas Medical Center in Houston, where they formed the totally separate Baylor College of Medicine. So, Baylor University, BUMC, and BCM are totally separate at this point and have basically only historical ties to each other. Some of the details may be off but this is the basic chain of events.