The "warrior" label worked for TR and it works for McCain. They were both military men.
But what pundits usually mean by "priest" is just somebody who they can't or don't want to describe as a "warrior."
Examples:
The Warrior and the Priest by Ron Brownstein
The Warrior and the Priest: How Clinton and Obama Divide Their Party by Ramesh Ponnuru
The Making of Hillary Clinton and Barack Obama by John Heilemann.
You're right. Henceforth:
"The warrior and the poser".