Brawl, Quarrel, Argument and Discussion

Solution 1:

An argument centers around a disagreement, and can be acrimonious. In a discussion, the disagreement is optional and acrimony is excluded.

A quarrel is a bitter dispute that may not be of a factual nature. The parties might just not like each other.

A brawl is a physical fight. Blows are exchanged.

Solution 2:

1. This makes some sense as an argument can be had without hostility, particularly in mathematical, scientific, legal, or other technical contexts. Brawl is really the only one that has specifically physical connotations though.

2. A discussion is a verbal exchange of ideas (as is an argument). However, an argument has more persuasive intentions and often involves disagreement and opposing viewpoints. A quarrel is some sort of dispute usually involving other people, but may or may not be expressed verbally. A brawl has physical overtones, usually meaning a physical fight or altercation, but at least refers to a very rowdy environment.

3. It seems surprising to me that "argument" appears less frequently than "quarrel", but I don't have data to show that your source is not accurate.