Conflict styles

Tangentially to this Captain Awkward letter, where the answer mentions that the writer's half-sister may have a different conflict style from hers, I started thinking about classifying conflict styles. It feels something like the Ask / Offer distinction in styles of communication (sometimes called Ask / Guess). It's useful to know that there is more than one way of doing it, and people whose style is different from yours are not necessarily terrible awful people who can't communicate respectfully.

The problem is I'm not sure there are two distinct approaches to conflict, or even what elements should be considered in defining conflict style. ( noodling about this )

So help me refine my ideas? What variations in conflict style have I not thought of? What approaches to conflict and argument do you find most productive? I mean, assuming that the arguers are already upset and you can't just magically all get along. Are there any ways of arguing that you think are just bad and should always be avoided?