know“知道，了解”，侧重直接性。

I know her very well.

我很了解她。

I don't know his current address.

我不知道他目前的地址。



know about “知道关于...的情况”

I happened to know about him.

我碰巧了解他的情况。

I don't know about that matter .

我不了解那件事。