How about this -
A snapshot is when you just want to take a picture with no care or knowledge of how it will look. You just want an image.
A portrait is when you take a picture with care and knowledge of how it will look. You want to convey emotion and feeling and not just have an image.
See to me that defines the two.
And it relates to an experience I had recently -
I went out for Mardi Gras to do some street shooting and because I am apparently ignorant of my past hangovers.
Now, a guy I work with was also heading downtown for Mardi Gras. I said we'd meet later, have a few drinks, etc.
Anyway, in the early part of the evening, I was shooting street performers and people in costume. What I did then was mostly portraiture. Without a doubt.
Later, I was drinking with my friend and some others. Then it was snapshots. Mostly because people kept posing....
But the images don't show anything other than people smiling. Where-as the images I took on the street show people being people and doing things.
Like the attached shot - Unconventional, but a portrait none-the-less.