The vids with the music are the actual match footages. the other non song equipped vids are older vids highlighting issues for the devs.
Well in STO, you're mostly grinding things like duty officers, or gear from STFs. Or getting up the scratch to buy your favorite toys off the exchange (auction house) PVE wise it's pretty much like any other mmo, just with instanced content.
Pvp wise, unfortunately there's no active struggle over any of these resources, etc.