In U.S. English I am not aware of ANY difference in meaning between a carousel and a merry-go-round.
Carousel is becoming more common, because it sounds fancier and more dignified. Thus, there are (wealthy) people who collect "carousel horses," not "merry-go-round horses," and in public parks the ride will officially be called, for example, the Greenway Carousel in Boston--but people will ask their kids if they want to ride "the merry-go-round."
I agree with Kevin about the playground ride.
A bit of outdated trivia. Kodak developed an extreme successful slide projector, that became almost universal from perhaps 1960 through 2000 for showing pictures at talks, presentations, and lectures. Their trade name for it was "carousel," because it used a well-engineered circular tray that held 80 slides and fed them reliably and quickly, without jamming. So you will occasionally see references to "a carousel" meaning "a slide tray."