My wife has actually had both, on separate occasions. About 15 years ago, she smashed her wrist, breaking it into multiple pieces. In the ER, they explained that the wouldn't give her an anesthetic to push things into place for a splint (to hold it together until surgery could be scheduled), but they'd give her meds so she would forget the pain. I was absolutely amazed that it worked. She vaguely remembers telling them "let's git 'er done" and then nothing for about an hour after that.

Fast forward about 5 years or so, she's on the operating table to have titanium plates inserted to hold her ankle together and she apparently wakes up in the middle of the procedure and started trying to rip her IV out while the surgeon and nurses struggle to hold her down (she's pretty strong) while the anesthesiologist puts her back under. She has no memory of this: the only reason we even know about it is that one of the nurses mentioned later that "you caused quite a stir in there."

Training horses is not for the faint of heart :-)