Sometimes there may be no difference at all between both these questions. At the same time, there may be situations where there is a slight difference between them.

 

“How are you?” is a bland greeting for someone you haven’t seen for a while, while “How are you doing?” may be an actual inquiry. The latter is more common when there is some expectation that the subject might not be doing well.

For example: “Hey, haven’t seen you in ages! How are you?” versus . . . “How are you doing: is the new baby still keeping you up all night?”

—cricketswool on English Language & Usage Stack Exchange

 Responding to how-are-you-type questions

—   How are you doing?

—   I am doing well. Or

—   I’m good.

“I’m doing good” is grammatically incorrect. If you say “I’m doing good” it could mean you’re doing some charity work or something positive.

You’re doing well or you are good.