An argument is a disagreement between people who may or may not know each other. People are sometimes calm during an argument, but they can become angry.
1. He and David had been drawn into a ferocious argument.
2. Money is notorious for causing arguments in marriage.
A dispute is a serious argument which can last for a long time. Disputes often take place between organizations, political parties, or countries.
3. Disputes over land boundaries, water rights, and debts are commonplace.
4. A similar dispute divided the party in 1975.
You can also talk about a dispute between individuals.
5. Their dispute raged for a week, Cindy becoming bitchier as it progressed.
Dispute is also used as a verb. If you dispute a fact or a claim, you state strongly that you think it is wrong.
6. Some learned historians today dispute his conclusions.
7. He disputed the legality of the invasion.