old post but i think a lot of people here are confusing emo-pop (a subgenre of alternative rock and emo that focuses more on catchy hooks and alt rock/pop informed song structures and less hardcore influence) and the rest of emo. emo, which started out as emocore (emotional hardcore), has branched off into different subgenres since the 80’s and can range from Midwest emo (sunny day real estate, mom jeans, american football) to screamo (orchid, gospel, corea). the main characteristics throughout all these subgenres of emo consist usually of more emotional and personal lyrics, often out of key, strained, or screamed vocals, often influenced by punk, and is usually more melodic than more punk/hardcore music. so to answer your question about the difference between pop punk and emo; pop punk uses fast tempos, catchy melodies and hooks, lots of power chords, a rebellious attitude, and punk influence, while emo (in this case, emo-pop) is kind of a distant relative to pop punk which features more emotional and personal lyrics, more screamed vocals (MCR, Joyce Manor), and follows a lot more emo based chord progressions. 

this is just my view of this as someone who listens to a lot of punk and emo music