“House Democrats’ novel conception of ‘abuse of power’ as a supposedly impeachable offense is constitutionally defective,” they wrote. “It supplants the framers’ standard of ‘high crimes and misdemeanors’ with a made-up theory that the president can be impeached and removed from office under an amorphous and undefined standard of ‘abuse of power.’”

Contrary to what Mr. Barr wrote 20 months ago, the Trump defense team also insisted that the framers did not want Congress to judge whether presidents abused their discretion and made decisions based on improper motives.

“House Democrats’ conception of ‘abuse of power’ is especially dangerous because it rests on the even more radical claim that a president can be impeached and removed from office solely for doing something he is allowed to do, if he did it for the ‘wrong’ subjective reasons,” the Trump team wrote.

A spokeswoman for Mr. Barr declined to comment. A spokesman for Mr. Trump’s impeachment defense team did not respond to a request for comment about the tensions.

But Mr. Barr’s view was no passing thought. His 2018 memo emphasized that presidents who misuse their authority by acting with an improper motive are politically accountable, not just in elections but also via impeachment.

Between elections, “the people’s representatives stand watch and have the tools to oversee, discipline, and, if they deem appropriate, remove the president from office,” he wrote. “Under the framers’ plan, the determination whether the president is making decisions based on ‘improper’ motives or whether he is ‘faithfully’ discharging his responsibilities is left to the people, through the election process, and the Congress, through the impeachment process.”

The result of Mr. Barr’s main argument in 2018 and the Trump team’s theory in 2020 is identical: Both posited that facts were immaterial, both in a way that was convenient to counter the threat Mr. Trump faced at that moment.