In 'Groundhog Day' Bill Murray's character said "I'm a god. I'm not the God."
What does "I'm a god" mean?
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The Oxford Living Dictionaries has these definitions for the word god:
(in Christianity and other monotheistic religions) the creator and ruler of the universe and source of all moral authority; the supreme being.
(in certain other religions) a superhuman being or spirit worshipped as having power over nature or human fortunes; a deity.
‘a moon god’
‘the Hindu god Vishnu’
Groundhog Day was set in the US where christianity dominates. That is, a lot of Americans believe in the "one true god". In the movie, Murray is saying that although he believes himself to be a god (definition #2), he is not the (christian) god (definition #1).
He is clearly referring to supernatural powers that he has somehow obtained, making him way higher over mere humans.
However, he qualifies himself, and warns that he is not G-d as the audience knows him. Not the one that people pray to, or that is responsible for creating the universe. Rather, he just has superhuman capabilities and powers.