Let me add to this by saying that even Bush was claiming, at the time, that he wanted to avoid war and that he needed the authorization to help prevent it. Yet most people now (and quite a few then) believe he was lying and that he was going to attack Iraq regardless of what happened.
Hillary has tried to weave her "I authorized force as a threat, not as a reality" narrative as a way to claim that she is both tough on national security but opposed to the Iraq War. Unfortunately, it is an argument that fails to achieve either goal.
One thing I learned from being a parent is that you never make a threat that you aren't willing to follow through on. Kids can see through hollow threats and eventually they become useless. If you consistently follow through AND hold off on making the threat until you are ready to follow through, then when you DO make the threat, the kid will take you a lot more seriously.
I think the same principle holds in foreign policy.
The whole authorize-the-threat is-not-equal-to authorize-the-war is an untenable position for any serious leader to adopt. It effectively tells any foreign enemy that your threats shouldn't be taken at face value. They can be finessed. They can be weaseled around. They muddle what is already a complicated situation.