Wisdom tooth anesthesia? What does it do?

2 days ago I had my 4 wisdom teeth removed (16 yrs old). I was given the three choices of anesthesia. I chose the last one, which is the one where you are put to "sleep" under an IV. My question is, is this anesthesia supposed to make you forget things? Because I forgot when I exactly fell asleep, but I remember the nurse putting gas over my nose and then the doctor inserting the IV into my elbow. The last thing I remember was the doctor saying, "we're starting to feed you the anesthesia, and your mouth will become dry and you will sleep." But I did not forget some things. I believe I woke up at least 3 times during the procedure. I don't think I was dreaming because all I saw were a bunch of blurry faces above me working on my teeth. I couldn't really hear anything and I was only awake for about 3-5 seconds when I woke up. When the procedure was over and I was wheeled to my parent's car, the nurse asked if I had a nightmare, and then I could have sworn she said, "You tried to hurt one of our nurses during the procedure." Now maybe I didn't hear her correctly because I was still out of it from being on the anesthesia, but I'm almost positive she said that. Could it be possible that I had done that? I honestly don't remember any nightmares from the procedure, I just remember waking up a few times. Can someone please explain the difference between general anesthesia and sedation? Which one was done to me? This was done in an oral surgery center, not a hospital. I just kind of feel bad if I caused that much trouble during the operation. The nurse also said I was moving/twitching too. I'm curious as to why the anesthesia made me act this way when I was under the IV.