Difference between the different von mises?

Which software do you use ? These output are likely explained in the documentation but generally speaking they refer to shell and beam elements having multiple integration points (or section points) through the thickness. For solid elements it's not relevant.

These are all 2D shell rectangular elements. Its not a popular programme I am using, its limited in its use, I dont think its possible to even use solid elements. With this being said, which von mises would you guess would be correct to use?

Also Ive been told to make the top plate thick, as it will distribute the loads more equally to the plates below - why is it that thick plates distribute load more equally than thin plates?

I would choose max since it's the type of output that we usually want to get. To clarify, this setting refers to individual shell elements so for example, top doesn't mean that you won't get output for the bottom plate.

Can you say more about the model ? The thickness of shell elements should depend on the dimensions of the actual structure. But it can be easily changed so you can try with different values and see how they affect the results.

a 2D shell still has bending, so top surface stress is not necessarily the same as bottom surface.

another day in paradise, or is paradise one day closer ?

in your example, I'd expect the highest stress would be on the top face, bottom surface (as the face has thickness, and a top surface and a bottom surface), near the load where the face has maximum bending.

another day in paradise, or is paradise one day closer ?

Top-plate top surface stress
Membrane- plate mid surface stress
Bottom- plate bottom surface stress
Max-most probably max value of stress between two-top and bottom surface

To check which plate has max stress, plot max stress( if above is true).

If the cube is made up of 6 faces with thickness and modelled as hollow shell cube , and you are applying load at the top face, I would expect the top plate to undergo bending, the vertical plates to undergo bending + axial compression and bottom plate to undergo compression.

Most probably stress will be max at the top plate(plate where load is applied)-top surface.

some programs display the VM as the surface that is visible so rotate model and see stress on other side