I've always looked at the shows this way:
-TNG as a sequel to TOS.
-DS9 and VOY as direct spinoffs from TNG.
-ENT as a prequel to every Trek series, but with a noticeably greater focus to being one to TOS in its final season.
I suppose ENT, TOS, and TNG could be looked at as a trilogy in the sense they all featured starships named Enterprise at roughly 100-year intervals, but otherwise there isn't really a unifying story between them other than that (no TCW in TOS and TNG, no Q in ENT and TOS). It might be argued though, that the three shows depicted the evolution of the Klingons from new adversaries in ENT, to old enemies in TOS, to eventually allies in TNG...