I thought this one was fairly clear to be "proper" plague
The Great Plague symptoms were very well described in literature from that period. It was unmistakably bubonic plague which is caused by only one bacteria - Yersinia Pestis.
This differs from some earlier pandemics which have little "medical description". In the early middle ages and before that people called nearly anything with 80%+ mortality plague. The only other diseases getting a honorary different mentioning were Smallpox and Cholera. So we in fact do not know if some of the earlier pandemics were real plague or let's say extremely virulent flu (middle ages version of the Spanish Lady).
Now, why the Great Plague was so great is a different story. Plague was not uncommon in the middle ages. A small epidemic here or there happened every few years. These however, did not become Great Plagues. While looking for an explanation of why a particular plague became Great in the bacteria looks plausible, the actual cause is more likely to be environmental - spikes and falls in rodent populations. Just like the mice spike in Europe this year (I have never seen so many, neither in UK nor Eastern Europe).