It is the case in NJ that unless you are a city you have one district with one BOE that controls the schools with budget, personal, hiring and firing. There is no difference between district and school board. It is a matter of semantics. The school board of education first answers to the municipal council then to the state department of education.
Don't be so sure. I looked at Massachusetts municipal law and it is not that much different than NJ about school boards and their powers.

