A projection is when you throw the person away from you rather than simply into the ground at your feet.
The late Fumio Toyoda did a version of 'kotegaeshi' where he would launch people away....a lot of people would call it a kokyunage though. Edit: If you youtube Fumio Toyoda kotegaeshi, you'll see a couple videos showing kind of what i'm talking about, but I've seen him execute it where he's not holding on to uke - a little more exaggerated than in the video. *here you go. Fast forward to 40:25...its around 40:30. At least thats what I was talking about. Far different than we normally would do a kotegaeshi at my Yoshinkan dojo. [ame="https://www.youtube.com/watch?v=ho34dj7g0nU"]Military Tactical Fighting Close Quarter Combat 1996 AIKIDO TOYODA / SENSEI DODARO MPEG - YouTube[/ame]
I remember Saito Sensei saying that eventually ALL nage techniques become Kokyu nages as all tech in Aikido as designed to develop and use Kokyu. Kote is a good example where you put a lot more Kokyu in the throw.
Last technique in this vid, I would call that a projected kote gaeshi [ame="https://www.youtube.com/watch?v=7rHntp2ATGE"]Takeno sensei and Koussoulis sensei from http://www.melbourneaikido.com.au/ - YouTube[/ame]
That's about how Toyoda Sensei would do it from time to time. On a side note, do you know what I'm talking about when I say the "running steps" version of kotegaeshi?