To absolutely correct the arguments stated below (and I might add, a year ago...), Light the Fuse and Run considered themselves a hardcore band. This would have been the way any of the bands that were influential to them such as Fugazi, 1.6 Band, Hoover, and most of what has been degraded out of the mid-atlantic hardcore scene from the late 90's with the term emo would have described themselves. The term emo has long been a lost cause, let Rolling Stone have it.
The third wave of emo doesn't exist... I mean, you cant call MCR, PATD etc, third emo wave, just because the majority think it's emo doesn't mean they play emo, it's a just a big misunderstanding, thats all. About the ska thing I have no idea, because i'm not into it :)
Emo makes a lot more sense when you look at it in waves like ska. First wave emo = screamo, second wave = sunny day real estate type rock, third wave = poppy MCR bullshit. Third wave emo is a horrible bastardization, just like third wave ska.