I think, technicaly, "To the Pain" actually means Exactly What It Says On The Tin- you are supposed to fight to wound, not kill, until the opponent gives up from the agony (basically an I Quit match with swords). Thats really what Wesley was threatening to do; it only became the way the trope is described, the "scare the hell out of the other guy" version, because he was dealing with a Dirty Coward of inferior skill and tricked him into thinking that he, Wesley, was in fit shape to fight, and the Evil Prince was so outmatched that a fight "to the pain" might as well be a torture session.

So...maybe make a Type 1 and Type 2?

These seem to be descriptions of Cold Blooded Torture rather than this trope; if someone is more familiar with them, please rewrite them to illustrate how they demonstrate To The Pain better.

• Naruto Itachi makes the victims of his Tsukiyomi suffer intense physical and mental pain for days on end, effectively breaking their souls and sending them into long comas.
  • Ibiki Morino anyone?
• In Fruits Basket it's revealed that when Akito and Yuki were both children, Akito locked Yuki in a dark room for days on end and beat him with a whip. During this time, Akito also subjected him to Mind Rape

Probably could use a mention of why this is often done: sometimes it's hard to see exactly what is happening, particularly with the poison variation. The description makes what is happening a lot more vivid to the audience.