You're a little off there. If you do use fanny to be anatomically specific, you're meaning vulva, not vagina.

But this varies wildly amongst non-Americans. When I grew up (London 60s) I got the impression that the fanny was the "front part" of a lady and the arse the "back part", "part" meaning a pretty big area. But then I was young.

In Canada, I am told by authoritative sources it means "butt crack" but I spent ten years there and I never heard that.