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.

Wake and wake up mean absolutely the same and are used interchangeably. Wake up is a little bit stronger in meaning. It is more often used in everyday speech.

Wake up is used as a command.

Wake up! It’s time to go!

👆Not “Wake”!