A flame can come in the form of an email, blog comment or post, class discussion comments or anyplace else on the internet. A troll is kind of a catch all term for trouble maker. There are many ways to make trouble. Posting flames is one way.
A flame is a specific type of action by troll. It's personal. An off topic comment is not necessarily a flame. A comment where you use someone's name in a deragatory way is a flame.
A flame is different than teasing or playful fun between friends. It's mean spirited. It's an attack, usually on someone the user does not know. Flames are started by trolls.
A Troll is a trouble maker on the internet. Flames are a symptom of the troll mentality. Troll mentality is negative, netiquette is positive. Insults distract from the merits of any issue. It makes the issue, it there is one, less important than the person.
If you are the target of a personal attack, flame, do not respond to it. It brings you down to their level. Stay above the trolls and flamers. Do not feed the flames!