Is not trying to kill synonymous with not fighting at full capacity?

Over the years some argue that character x is holding back because they don't want to kill character y.

No. All it means is that the person is not trying to strike at the vitals. It has nothing to do with how much effort or exertion they're putting into a fight.

It really depends on the situation, but in most cases even if you aren’t aiming to kill an opponent that doesn’t prevent you from going all out with the objective being to simply incapacitate him.

MasterCilghal wrote:It really depends on the situation, but in most cases even if you aren’t aiming to kill an opponent that doesn’t prevent you from going all out with the objective being to simply incapacitate him.

This pretty much. Though sometimes it can be harder to just try and incap rather than kill.

No. However, if you're toying or testing someone, you're most likely holding back. Not trying to kill doesn't stop you from disarming them or subduing them, albeit it's entirely dependent on the circumstances.

Limiting yourself to non-lethal attacks means that you aren't fighting to your absolute best, even if you're doing your best relative to your self-imposed restrictions. However, note that some characters would be less hampered by fighting in this manner than others, to the point that they might be operating close to their full capacity.