[1] Generally the term Screamo refers to a branch of hardcore popularised in the 1990’s by bands such as City of Caterpillar, Envy, Orchid, Saetia et al. Often features dischordant riffs, high-pitched screams, some spoken-word vocals (Saetia were known to utilize this technique quite often), and quite often the recordings were very lo-fi, and grainy.
However the term has been heavily popularised by MTV as a reference to the pop-punk/emo bands of the new century (Finch, Story of the Year etc).
[2] screamo is a term that refers to recent bands that play old style emo. Most pinpoint the first use of the term to Saetia. When the media started to label pop punk and indie rock bands emo, people needed a new word to describe the style of music that used to be characterized with emo. Some say screamo is a little more artsy and pretentious than older emo, but that’s arguable.
Nice bit of explanation spotted on an emotorrents.com discussion thread. Now if I could only figure what emo is …