The breed you are likely thinking of is simply called the English Bulldog. It is the only recognized bulldog breed.
You might be getting the two confused because the modern English Bulldog is a much different breed than the dogs that were bred in England centuries ago. The older dogs were more athletic and agile, with a different build and temperament.
Here's a quick breakdown:
* "Old English Bulldog": This term isn't officially used. It might be a way to refer to the older, more athletic type of bulldog that was popular in the past. However, there is no modern breed recognized with that name.
* English Bulldog: This is the only recognized bulldog breed today. They are much stockier and less agile than the older dogs, known for their wrinkled faces and brachycephalic (flat-faced) features.
So, in short, the modern English Bulldog is the breed that descended from those older, more athletic bulldogs. The term "Old English Bulldog" is not used officially.