At loggerheads and At variance

At loggerheads adjective - In a dispute or confrontation.

At variance is a synonym for at loggerheads in fighting topic. In some cases you can use "At variance" instead an adjective phrase "At loggerheads", when it comes to topics like in disagreement.

At variance adjective - Not in accord.

At loggerheads is a synonym for at variance in conflicting topic. You can use "At loggerheads" instead an adjective phrase "At variance", if it concerns topics such as fighting, in disagreement.