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I think Swamp Thing originated in comics in the early 70s. The movie came out in 1982. Written and directed by Wes Craven and featuring Adrienne Barbeau's body (who was, I think, married to John Carpenter at the time). Carpenter wrote 'Escape from New York' (also starring Barbeau's body) which came out in 1981.

Alan Moore was one of the British invasion of genius comic writers who did makeovers of old titles/characters from old mainstream American comics. So, yes, there's a relation. Alan Moore wrote the first many issues of the "new" Swamp Thing series (in the early 90s I think). This film is the original shit though.

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Like an arrow,
I was only passing through.