Here in Florida, charter schools are quasi-public schools but have some differences

A) they do not normally get local county funding. Their money comes from the state and federal level (mostly)

B) they are not a neighborhood school and can specify who they will accept. They can also focus on specific skills. Miami has a rather famous arts charter school, we have local charter schools that are bilingual, and we have one up the street that focuses on math and technology. These are the main stream charter schools that have done well. Charter school failure rate in Florida is something like 30% and has lost about $70 million (out of a 700 million budget).

C) they are not held to the same state standards - but must comply with federal standards. (And this was one of the reasons why Devos was hammered in her hearing when she said it would be left to the state to impose standards. Many places, like Florida, rely on the charter schools to comply with federal enforced regulations)

Private schools are not funded by the gov't, but do accept state dollars here in Florida for low income scholarships (Step up Student). Not all private schools accept these scholarships.