What Roddenberry said: Starfleet is not a military organisation.
What JJ Abrams (together with most subsequent Star Trek writers) heard: Starfleet is definitely a military organisation.
What Roddenberry said: The Federation operates on a moneyless economic model.
What JJ Abrams heard: The Federation operates on a capitalist economic model.
What Roddenberry said: The Federation is a futuristic, post-scarcity utopia with no poverty or bigotry.
What JJ Abrams heard: The Federation is the United States of America in space.