A disagreement is a type of conflict, either between people or ideas. No it’s not! Yes it is! It’s an argument. If your opinion contradicts the facts, there's a disagreement.
When ideas conflict, there's disagreement. If you want to go to an action movie, but your friend wants to go to a romantic comedy, that's a disagreement. Statements, opinions, and claims can also disagree. If I say my grandmother was a sweet woman, and you say she was a horrible person, that's disagreement. If the IRS finds a disagreement between your taxes and your real income, you could be in trouble.