This book says
understand someone并没有“理解某人”的意思，只是“懂得某人的话”之意，如：If he had spoken French I would not have understood him.（要是他说的是法语，我可就不懂他的话了。）汉语中现在常说的“理解万岁”中的“理解”可译成understand about (someone)，如：You don't understand about me.（你一点也不理解我。）这里理解的不是指所说的话，而是指一个人的心情、做法等。Her parents really understood about her situation.（她的父母亲真的理解她的处境。）
that "understand someone" means "to know the words that someone is saying", like
If he had spoken French I would not have understood him.
and that "understand about (someone)" means "to know how (someone) feels, behaves and etc.", like
You don't understand about me.
Her parents really understood about her situation.
But I find many dictionaries say that "understand someone" can mean "to know someone's character, how they feel and why they behave in the way they do", like
He doesn't understand women at all.
My parents just don’t understand me.
and that "understand about something" means "to know or realize how or why something happens, how it works or why it is important", like
Doctors still don't understand much about the disease.
So are there any differences between "understand me" and "understand about me"?