quarrel = orally / fight = physical quarrel: an angry argument or disagreement between people, often about a personal matter: a family quarrel He did not mention the quarrel with his wife. They had a quarrel about money. Were you at any time aware of a quarrel between the two of them? fight : 1- to take part in a street, a war or battle against an enemy: [v] soldiers trained to fight He fought in Vietnam . 2- to struggle physically with sb: [v] My little brothers are always fighting. She’ll fight like a tiger to protect her children.

fighting may involve beating someone up :P

quarrel= argue fight= usually physical

Almost the same. Fighting can mean hitting each other.