Often times, most people ask these questions interchangeably. I ask these question separately. To me, they are separate questions.
How are you? -- How are you doing,, how are you in the moment,, how is your mental and emotional state at the present time of questioning. How you doing with a certain stage or thing or facet.
How are you feeling? -- How is your body feeling, how are you feeling in the moment...Yes, the two may seem redundant, but they can be importantly distinctive questions. A person can be doing just fine and feeling horribly. In vice versa, they could be feeling amazing but emotional drained. Also, the questions can go hand-in-hand...Somebody could not be okay with a certain situation or happening, yet FEEL that no action may need to be taken.
So...how are you? How are you feeling?