If someone ever says cuboid it means a fully functional puzzle. It doesn't say anything about shape shifting yet though. A fully functional 3x3x4 doesn't change shape simply because a 90° of a 3x4 face obviously leads to a block of the mechanism. So cuboid can change shape but it depends on the dimensions.
There are also exceptions. For example there are 3x3x2 cuboids, I believe invented by smaz, which can change shape. I don't really know how.