neither of those songs really identify as emo though... i cant explain it, but coldplay is just alternative, and nickelback is alternative rock.. though the term has been dropped one or two times, nickelback is by no means "emo".
i recommend you to look up emo on wikipedia, that'll give a better explanation than i can do
Quite, Wiki explains alot of things, it's a good shot if you really want to see a really good description of Emo (If it the article is written properly). I know it used to be just a music type, then it became a style followed by it's pejorative evolution. People often point out unusual artists with 'unique' clothing styles as Emos, Panic! at the Disco is a great example, but I don't think they are.
I listen to Electro/nica, Rave and House, all pretty similar. I mostly listen to Crystal Castles, Ratatat and Justice, tough Ratatat is just qualified differently by alot of people, I consider it in one of those styles. Electro varies alot between artists, but the sounds they use is what qualify them into those groups. When my siblings hear some of my music, they tell me to turn the volume down or use my headphones (Tough they lower the sound's quality). My brother and his girlfriend just hate it when I listen to it, may it be for five seconds. I don't know if it's the music that makes them unlovable, but they really don't appreciate it.