On family friendly sites or places with big-ego staff I notice disagreement to be very easily termed as flaming. I disagree frequently and am not opposed to challenging someone's beliefs or chasing them to back up their statements (the latter of which I was warned recently on a site for doing, or as the moderator put it, "encouraging a flamewar" or something similar). I engage in debate and don't moderate my position to suit people who want to be cuddled, but I will have a healthy respect for the other side. A flame war happens when both sides are flinging words that serve to no end; those words usually being insults. 

In short, I think it just depends on the community when it comes to how the broad definition can be painted.