A bit of both, really. Grammatically, "I get it" is the same as "I understand" and "I got it" is "I understood" ("get" being present tense and "got" past tense. - "I didn't get it for a long time, but I finally got it")
But "I got it" can also mean "I understand" in the sense of "I didn't understand before, but I understand now." ( "I didn't get it before, but I've got it now.")
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But "I got it" can also mean "I understand" in the sense of "I didn't understand before, but I understand now." ( "I didn't get it before, but I've got it now.")
Does that help?