The common denominators throughout the bais yaakov system are their rule books and their ideal end products. Uniform, no talking to boys, tznius, good middos, and being taught the majority of your school subjects by Rabbis and rebbitzins.
Those are common denominators, but I would most emphatically say that they are NOT what makes a school Bais Yaakov. They are the outer trappings of what makes a Bais Yaakov, and can vary from school to school. What unites all Bais Yaakovs is that they have certain hashkafos about Torah and the role Torah should play in your lives that try to imbue their students with. The rest is just commentary.
Also, I have to say that I went to a pretty mainstream Bais Yaakov high school (there isn’t a single person here who would contest its Bais Yaakov-ness), and the majority of the teachers were NOT rabbonim/rebbetzins (the male contingent was mostly rabbonim, but there were very few of them). And all the female teachers vehemently protested the title (even the ones who probably deserved it).