Apart from Christmas grottoes for kids, we sometimes use the word to refer to certain famous grottoes, such as the Blue Grotto on Capri, an Italian island. In the minds of English speakers, we think of caves as being dark and scary, while grottoes are decorative and magical.

Santa.

Grotto is a very rarely used word in English. A grotto is a small, attractive cave but I would almost always use the word cave instead. The one exception is when you are talking about Father Christmas / Santa. His home is called Santa's grotto.

"Cave" is a plain, factual word that's basic English vocabulary. "Grotto" is a colorful word and it's not basic English vocabulary. "Grotto" has two slightly different meanings. It can be a small cave. It's a loan-word from Italian and sounds exotic. As Su.Ki says, it carries overtones of being a special place, magical,, sacred. I am most familiar with it in place names--I would not normally talk about a "grotto," but when my wife and I visited Canada there was a cave on the Bruce Penisula named "The Grotto"--so of course we call that "The Grotto." A "grotto" can also be a cave-like manmade structure, often ornately decorated, often religious, such as the Dickeyville Grotto in Wisconsin: http://www.dickeyvillegrotto.com