This 100%. Another big difference can be independent school districts - for example, the Clark County School District employed nearly 20k teachers in 2017, while BPS, which is part of the City of Boston, employed a little under 7k.

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Local government can be structured in so many different ways that if you just look at a wikipedia article or facebook listicle you will easily be led astray. If OP wants to do actual research, start with the Annual Survey of Public Employment and Payroll from the US Census.