While the two terms sound interchangeable, “how are you?” and “how are you doing?” are, in fact, two very different questions. Don’t believe it? Check with the person you just asked.
“How are you?” has become something of continuance to “hello.” It seems to flow naturally off the tongue and most of the time, it’s a question that does not really beg an answer. Ask yourself if you really care to know how they are? Probably not, it’s just part of your greeting. And you certainly don’t expect an actual answer.
On the other hand, “how are you doing?” is used when someone genuinely wants to know. It isn’t the common phrase used after an introduction; it’s what you use when you want to check in on a person. You aren’t quickly moving on to something else, asking “how are you doing?” strikes up a conversation.
Another difference is what each phrase phrase refers to. This can be exampled through a person who is sick with a disease that they had no side effects for. “How are you?” can be answered with, “I’m fine” as they are physically feeling fine. But “how are you doing?” impresses the idea of emotion. “Well, I feel great on the outside, but on the inside, I am torn up.”
While the differences between the two phrases are very subtle and can certainly be argued, in making the choice of which to use, ask yourself who you are addressing and how you want to be perceived.