Example : He had a dispute with his wife.
There were irreconcilable differences.
The familiar conflict between Republicans and Democrats.

Synonyms : conflict, difference, difference of opinion

Synonyms : contravention

Example : She challenged his claims.

Synonyms : challenge, gainsay

Example : We quarreled over the question as to who discovered America.
These two fellows are always scrapping over something.

Synonyms : altercate, argufy, quarrel, scrap