You'll hear lots of different names for grips. Different people also use the same name to mean a different grip. This can be confusing.
Badminton England have standardised on the following grip names: basic, thumb, panhandle, and bevel. You can read about them in my
grips guide.
As I understood it, the "pinky grip" wasn't so much a specific grip, but more an idea about how you use your last two fingers (ring and "pinky", or "little finger") as the main fingers for securing your hold on the racket. Your other fingers also hold the racket, but they are a little more free to move.
As far as I know, this is pretty standard. It's often helpful to use these two fingers at the beginning of the grip tightening action: use them to snap the racket butt into the palm, which creates a rapid pivoting movement over a small distance (this is particularly emphasised by the Chinese coach Xiao Jie, and I was also shown something similar by Yvette Yun Luo at the 2007 England coaches' conference, in a workshop about grip).
This "sling shot" method mainly works with the basic or bevel grips, and not so much with the thumb or panhandle grips.