The basic concept is:
内側 means that spaces are divided by something like fence, and you're standing the inside ground, while 中 is like that there's a vessel and you're inside of it.
The interpretation of Xの内側 and Xの中 is different regarding the X. In the former, X indicates boundary, while in the latter, X is container. If X is something with inner room, then whoever in Xの中 is likely to be in that space, but if X is a filled material, then they're likely to be packed within it.
Random examples taken from Google image search:
They are thought to be in ガラスの内側 but not ガラスの中:
while he is thought to be in ガラスの内側 or ガラスの中:
and they are thought to be in ガラスの中 but not ガラスの内側:
(well, these are actually ice cubes but never mind)
Extra
There's other (mostly figurative) usage of 中, that is you can refer what you see through apertures such as: 絵の中, 鏡の中, 画面の中 etc.