There are always variations on names for things, but I find when it comes to different grip positions, each grip might have more than one name, but each name tends to be specific to a certain type of grip (if that makes sense...).
So, having said that, I'll try to explain these grips to you regarding my understanding of them. If other people have different names or understandings, feel free to share as well.
Cup Grip - aka True grip/Chinese grip. In a cup grip, your thumb is wrapped around the pole in the same direction as your fingers (I like to think that you are cupping the pole this way, instead of grabbing it).
Split Grip - In this grip, your thumb is wrapped around the pole opposite your fingers (like you are grabbing the pole, not cupping it).
Twisted Grip - In this grip, your top hand is twisted around to grab from the other side of the pole. An easy way to walk yourself into position to get the idea of it is to grab the pole above your head, and then without moving your hand, twist your body away from that arm (so if you are holding the pole with your right arm, rotate your body to the left, or counterclockwise) until you wind up tucking underneath your holding arm. Now that hand is in twisted grip.
Elbow Grip - pretty much anything that involves the elbow pit as a contact point for one of your arms
Forearm Grip - In this grip, you have the pole making contact along your entire forearm.
I'll make a quick video and upload it tonight for you to clarify :)
