Shadow is a different style of RD compared to the traditional (compare M591 and M592). It carries the cage in front of instead of inside of the parallelogram allowing it to fold in tighter, and allows for bigger rear gears up to 36 tooth. Pretty much all the RD's at 10 speed are Shadows, there are a few at 9-speed (M592 and M4000 for example).

Shadow+ includes a clutch on the pulley cage, helpful for full suspension bikes and 1x10 setups. You can see one if you compare RD-M610 to 615. Only available on the 10x or higher speeds. Incompatible with 7-8-9s because...

Dyna-Sys is longer cable pull shifters used for MTB 10-speed and above, which don't match the old SIS standard that was in use up through 9-speed. You can see the difference in the lever arms at the back of RD-M610 compared to 592.