I can't offer much on this subject beyond what I've already noted elsewhere. I wonder if you might not be stumbling on artificial taxonomic terminology, Rachel? A portrait is a personal representation with an agenda, as your two examples illustrate well. Your theatrical head shot probably had to fit within specific proportions, and feature mostly head, for program repro consistency, eh? (You look a bit like
Helen Mirren in that shot. You're a lovely lady!) But that second portrait clearly has a very different purpose, so much that it's very difficult for me to see that it's the same person.
Most portraits, photo and other, are created for, and towards, a purpose. Identification (photo i.d. "portraits"), self-promotion (theatrical head shots), fashion promotion, and, yes, personal vanity. But, once again, it's worth noting that the sitter/subject is generally not the audience.
A parallel, but somewhat related, remark. I have been working with a museum on a Japanese photography history project that encompasses every type of photography throughout Japan's photographic history. Lots of studio portraits as well as landscapes, still lifes, etc. After looking at thousands of images one attribute jumps forward to me. Western photographers have been oriented towards portraying how their subject
looks, perhaps owing to photography's early roots in Western journalism. But Japanese photographers seem oriented towards capturing what something
is. It's a subtle distinction but one that becomes obvious after a while.
That distinction applies very much to portraiture. The most revered portraits capture what someone is, more than how they look or want to look.
Yousuf Karsh's famous portrait of Winston Churchill came about when Karsh pissed Churchill off by insisting he take the stogie out of his face. Churchill became indignant...CLICK! Perfection. Karsh captured a glimpse of the essential persona that made Winston Churchill one of history's great figures.