Debating is a kind of game, with formal rules and the objective is to win. The actual issues are relatively secondary, the point is to show that you can be more effective in dealing with them. And the assumption is that opponents should treat each other with respect, and play by the rules, with mutual respect being one of the rules. That needn't exclude fairly robust play any more than it does in other games. And it doesn't mean that the outcome may not matter quite a lot, and that cheating may not come into it.
A discussion is something different - the actual issue or issues are central, and the object is for people to bring to bear their different perspectives on exploring the issues, and advancing their understanding. Once again, hostility has no place.
Quarrels or arguments (in that sense) are what we get when a debate or discussion degenerates and turns into a real fight, in which the excercise of skill or the pursuit of truth is abandoned. Any time that happens it's a failure on the part of those concerned.
Typically often enough it is onlookers and the people on the outside in contests who are more liable fall into that trap. In sport and in politics fans can get quite taken aback when they see that the actual players can get on quite well with each other. The same thing happens with rival advocates in court cases.