Forcecage only cares about the space (threat range, actual size, or otherwise) a creature takes up in its environment.
This is often measured on a grid. Medium creatures take up a 5 X 5 'space' even though they are not 5ft wide. This represents a Size that is 'Medium'. Large creatures take up a 10 X 10 'space' . So on an so forth.
The Force cage has one of 2 maximum dimensions: A 20 X 20 Cage with 1/2 inch spaced bars a 1/2 inch thick, or a 10 X 10 cube completely sealed and solid.
The spell cares about if a creature's size threshold (the dimensions it takes up as a result) fits within the chosen form. Any creature larger than 20 X 20 if cage is chosen or 10 X 10 if cube is chosen does not fit and is not 'completely inside the area'.
I am not at my computer and forget the relevant size categories but any creature 21 X 21 and larger would not fit.
It also bares mentioning that the measurements of Forcecage are 'on a side' or per side; which includes the top or 'ceiling' if you will. Creatures who fit within the maximum 10 X 10 or 20 X 20 may not be short enough to fit under the cage or cube, though this is conjecture because nothing stops you from having a very tall Goliath break the height measurement of a 'Large' 10 X 10 creature. This flavor does not then make that Goliath take up 5 X 5 X 10. It would still fit within a 5 X 5 forcecage. Unless your DM wants to add a height measurement to every potential creature because we feel flavor matters?