Captain America's Movies, Television's Agents of S.H.I.E.L.D.: Which One Is the 'True' One?

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I say 'true'; I mean 'as happened in the Marvel Universe'---in the movie, S.H.I.E.L.D. was "compromised" by the leader who helped start it (not Nick Fury, but some secretary-of-security ...and Agent Coulson was nowhere to be seen!); on T.V., S.H.I.E.L.D. was 'compromised' by double-spies from H.Y.D.R.A. (or were they just named THE WORD "Hydra"?); and Agent Coulson rebooted `em. Or do they both exist in the same Marvel Universe? If so, how?; if not, which one survives?