> Charter schools are public schools, just managed by private organizations.
Charter schools are publicly-funded schools exempted, via the grant of a special charter (hence the name), from some of the generally-applicable rules governing the public school systems of which they are a part (which particular rules exceptions are made for varies from charter to charter.) They may be publicly operated, operated by private for-profit enterprises, or operated by private non-profit enterprises.
> And it's not a situation where only rich people can get their kids into charter schools.
While that may be the case, among the rules that charters are often exempted are ones which prevent them for cherry-picking students on grounds which, while they may not directly relate to wealth, are strongly correlated with it.
> Charter public schools are concentrated neighborhoods with mostly minority populations.
That's actually part of the problem that minority-interest groups have with them; among the problems that this creates is that they often displace schools that are subject to the normal public rules from those areas, forcing children who are not admitted under the charters rules to go to more distant traditional public schools than they would have to if the charter did not exist. (Another is that, for less-selective charters, members of the population may be effectively coerced into attending the charter as opposed to a traditional public school by the lack of access to traditional public school caused by the charter placement.)