Translation:I caught a cold.
In everyday language, "caught a cold" and "got a cold" sound so similar that they are used interchangeably. I would counter that some people would definitely understand you saying "caught a cold" but would never use it. (Compare with "I feel like I'm catching a cold" vs "I feel like I'm getting a cold")
People will get the idea, but they will get the wrong idea:
"I caught a cold" - I became sick with the cold. I am likely to still have the cold but I might have gotten better. (Consider "I caught a cold last year in winter." If it's summer now, you probably weren't sick for that long)
"I got a cold" - I definitely have the cold now. I did not get better. ("got" means "have" in a lot of sentences)
I disagree. I can say "I got a cold" to mean the same thing as "I caught a cold", even if I don't have it anymore. I could say "I got a cold right before Christmas, but it's gone now".
If I said "I've got a cold", it would mean "I have a cold", but if I say "I got a cold", it just means the same thing as "I caught a cold".
(I'm a native speaker of Canadian English.)