They are not "I get it." or "I got it.". They are only "Get it." and "Got it.". I'm wondering what's the difference between them.
closed as not a real question by onomatomaniak, Andrew Leach, tchrist, aedia λ, Matt Эллен Apr 26 at 21:03
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Get it on its own would normally only be used as either an imperative (telling someone to get something) or a question (asking if someone understood; [do you] get it?). I get it (meaning I understand) is not usually shortened to get it.
Got it can be used in a few more ways. As a statement ([I've] got it), it means that the speaker understands, or the speaker physically has something, or (in a similar way to I've got this) that the speaker has the situation under control.
As a question ([have you] got it?) it can be used to ask any of the above: if someone understands (the same as get it?), if they physically have something, or if they have the situation under control (like have you got this?).