Closed Timelike Curves vs Time Loops: What's the Difference?

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TheQuestionGuy14
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What's the difference between Closed Timelike Curves seen in physics and the time loops in movies where a character relives a period of time over and over, but retains memories? I'm just curious about this stuff.
 
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One is probably fictional and the other is definitely fictional.
 
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Dale's answer is best.

I'd add that there is no science - or even logic - in the time travel of almost all shows and movies. The (psuedo)science is simply tortured into a format that makes for a g̶o̶o̶d̶ plot.
 
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