In medieval Europe, war was generally guided by a code of conduct known as the bellum hostile. However, not all humans felt that they were bound by the traditional Western chivalric code of conduct, and so a second code of conduct emerged, the bellum Romanum (or sometimes, the guerre mortelle).
The bellum Romanum was war fought under the rules that the Romans had used. While bellum hostile barred the enslavement of prisoners and encouraged good treatment of captured nobility, bellum Romanum did not. To some extent, the Roman system was essentially the same as the European, with the primary difference that the Roman system treated all of their enemies in the way that the Europeans treated their peasants. While members of the nobility surely saw this as a significant difference, to modern readers the primary bit of civility added under bellum hostile was that the weak were killed or ignored, rather than enslaved.
There were other differences, of course. Under bellum Romanum no special effort was made to exclude non-combatants from the violence, and under bellum hostile massacres and torture were... discouraged. By and large. Unless it seemed prudent, and as long as you limited the atrocities to the lower classes.
While there were any number of instances of battles fought under bellum Romanum, the most famous were no doubt the Crusades. There were also some circumstances in which good Christians might decide to waive the bellum hostile, as with Joan of Arc's forces at Orleans, but this was the exception rather than the rule. However, if a combatant did want to waive the civilized code of war and fight like barbarians, the established way of doing so was to march into battle under a red banner.
The related term guerre mortelle is usually treated as a synonym, but translates from French as 'war to the death', and was often used particularly to refer to revolutionary war, civil war, and declarations of 'mortal enmity' (akin to a duel), which were, in spirit, less noble than the territorial battles of the knighthood.