The Allusionist: 8. Crosswords

https://overcast.fm/+EBCBG5fQU

This episode is all about cryptic crosswords. My question, even after listening to the whole thing: Is a “cryptic crossword” just what they call regular crossword puzzles in England? Or is it somehow different? 

(Just Googled it and, yes, they are different. The clues need to be more puzzle-like than a typical crossword puzzle.)