These phrases mean the same thing they mean in other contexts, and they are just as subjective in this context as in others.
If a new xế hộp model is based on an old one, then some part of the old design was used in some fashion, perhaps directly, perhaps modified, perhaps just as an inspiration, when designing the new one. If a fictional story is based on a true story, same idea - fictional story inspired by and containing many similar elements, some maybe modified, as original true story. Etc. Same with "derived from", although that usually implies the case of "based on" where modifications were done lớn the original (with some extras).
So if OS B is based on A, some unknown significant amount of things from A were used when B was created. Perhaps code, perhaps user-interface design, perhaps philosophies, etc.
An opposite of sorts is starting from scratch. If B is some brand new concept, designed from the ground-up with no major source of inspiration and no components from A, then B was neither based on nor derived from A.