Extradimensional and non-dimensional terms are interchangable.
Leomond's secret chest is the foundation spell by which all magic containers that function like a bag of holding are formed, but the chest itself does not have the non-dimensional tag, nor does it reduce the weight of its contents, nor is it described to have a weight limit. Space seems to be the only factor, with no penalty mentioned for exceeding that capacity.
A belt of hidden pouches, bag of holding, heward's handy haversack, chest of holding, each of these are defined as to be an extra dimensional/non-dimensional space.
The secret chest is described as non-magical by the spell, whereas the bag of holding types are magical.
The chests are nonmagical and can be fitted with locks, wards, and so on, just as any normal chat can be.
Can Leomond's secret chest be summoned while resting in a rope trick?