Who You Are: There are things you do because of your intrinsic nature. You are who you are. That's the kind of person I am!
What You Are: There are things you do or want to do because of things you have no control over. Victims of circumstance is what you are. I do what I have to do!
Examples
Army officers: Attention!
People who spent most of their lives working in the army come to expect similar levels of discipline and no-questions-asked obedience in their personal lives as well. They expect you to listen to what they have to say (Attention!) and this is what often leads to coffee-table monologues!
Beggars: What kind of cheapo are you?
A beggar pleads with you for money persistently. Finally, you are touched and finally give him small change. Then It has happened to me!
Beggar: Please...Please...Please... (What You Are: Beggars beg)
You: No...No...No... (What You Are: Refuse requests for money from strangers.)
Then you finally give in...give him small
You: Here take this. Hope this change helps. (Who You Are: Human being with empathy)
Beggar: What? 50 paise!!! (Who You Are: I gave up my dignity for this!!??)
Crux
There is an Ego associated with both these components of our personality and this leads to conflicts and problems. Our irritation with people we interact with usually expresses itself with the protests: Who does he think he is? What does he think I am?
It is easier for the What-You-Are component to override and control the Who-You-Are component. I guess how comfortable you are with the sudden switch-overs will determine how happy you are...