Townships only exist in New Jersey and Pennsylvania; most of the rest have counties. As you say, it varies from place to place; any of them could start a fire service if the residents vote for it and fund it via local taxes.
Ohio has townships within its counties; they serve as a catch-all for areas that aren't otherwise incorporated as cities/villages, and that can make a big difference for local property tax and services.
Townships exist in most states - only the original 13 colonies don't have them. they are a federal thing, and how land was surveyed (IIRC is dates back to the Louisiana Purchase, but I can't find verification in a quick search. How each state use them differs, but the concept of a 6 mile by 6 mile section of land comes from the federal government. Originally one section (1 square mile) of land was set aside for the local school to own - some would be sold to build the school and rent from the rest would provide for the school teacher's salary.
Most states also have a county, but this is different from a township. New Jersey and Pennsylvania (as part of the original 13 colonies) don't take part in the federal township system and have their own system with the same name that is otherwise not related.
