I always thought they were the same thing with different names, but it sounds like there is some debate to whether these were two different things entirely. In my last History class in college the Professor mentioned how there could be two sides to this subject.
I hear that they spread differently and also have different death totals, but the symptoms were alike? Where do Historians fall on this subject?
The Black Death refers literally to the pandemic that hit Europe in the 1340s. "Plague" or "The Plague" is the non-medical term for the disease that caused that Pandemic. There were multiple resurgences of it after the 1340s. There is some controversy over what the pathogen that caused the Black Death and the subsequent epidemics.
There has been testing done on mass graves of plague victims which indicates that a bacteria called Yersinia pestis is the culprit for the Plague. However, there has been some debate about whether Y. pestis is the cause for both the Black Death and the subsequent bouts of plague that hit Europe.
It's a bit hard for historians, like me, to conclusively examine that research, as it has been carried out by archaeologists and biologists, fields we aren't trained in. It is my understanding that most researchers believe that Y. pestis is responsible for the Black Death, and that only a small subset of researchers (sometimes called Plague Deniers) believe that another, possibly undiscovered, pathogen is the actual cause.