There's one more structure that's (so far) exclusive to the UK: the Charitable Incorporated Organisation [1].
It can be founded as either a foundation (trustees and voting members are the same) or association (usually a larger group of voting members).
The key advantage of a CIO versus a CLG are the less onerous compliance requirements, which go a long way towards keeping smaller charities cheaper to run.
[1] https://en.wikipedia.org/wiki/Charitable_incorporated_organi...