They are all "ego" batteries. Ego is not a brand name, but a class of battery.
The "C" refers to "cartridge" used on top of the battery, so not really a difference in the battery itself. Usually means an atomizer/tank system, rather outdated by today's standards.
The "T" refers to a "tank" used on top of the battery, usually a clearomizer.
"Spinner" and "Twist" are models of variable voltage Ego batteries. Spinners made originally by Vision and Twists made originally by Joytech. These have also become generic model names as well.
If I'm incorrect on this point, please correct me.