http://en.wikipedia.org/wiki/Screamo
It's called screamo because back when it started it was a more aggressive form of emo. Screaming alone does not separate emo from screamo.
Emo bands can scream, but they don't necessarily have to.
Emo tends to be more dynamically driven. A good example of a quintessential emo song is "Seven" by Sunny Day Real Estate (
I do think all of the genre-ification can get a bit silly, especially when the same genre titles are rehashed multiple times with different generations of artists, but I also think there is some worth to all the sub-genres in that it helps people find similar bands to things they already like more easily.