Cross mount is like side control except that you have both your elbows on one side of the opponent and both your knees on the other side. I don't know what triangles are meant from there but technically it is figure-four or triangle used to submit when applying a Kimura, Omaplata, cutting armbar, or key lock from that position.
Side control is when you are on the side opposed to cross mount when you are lying across the body. Typical side control is one arm under the head of the opponent, the other arm is blocking at the hip (preventing them from rolling into you). Side control generally applies pressure to the opponent's shoulder by driving into their chin with your shoulder. This pressure should immobilize the opponent's closest shoulder to the ground. But side control can be used generically to mean anytime you are on the side of the body. Even cross mount can be described generically as side control. The only reason to label things differently is when talking about submissions and such. For instance, when moving to cross-mount this is usually to get a submission. It is not a good position to be immobilizing someone because it is hard to apply a single point of pressure from this position. Also from the side you have other positions such as scarf hold, etc. Gah, I go to the mighty wiki to find a definition (http://en.wikipedia.org/wiki/Side_control) and I see this picture: This is labelled as side control, however, to me this is actually a mix between cross mount because the person is lying across the body and side control, because the far arm in blocking the hip. In fact, IMHO, the above picture does not show a very good position, but more what would be a transitioning position between side control and cross mount.
Sorry, I know we all use different terminology, hell I'm not always consistant in what I use Cross side - modified scarf hold. DOne like this: http://innovativema.ca/forum/view.php?pg=crossidetriangle
Sorry. But it just seems like your "cross mount" is a slight variation on side control. There are numerous possible differences between one side control and another, but naming all of them would get confusing.
That's what we call "scarf hold." Yes it is a form of side control but pressure is applied above their right hip to immobilize instead of their right shoulder/chin. Pictures help, so even if we don't call things the same thing, we can see what others mean.
