The riddle
What Do You Call a Sleeping Dinosaur?
Saur against snore
Dino is the same in both words. The ending is the part that changes: dinosaur ends in -saur, a vowel sound after an s, and dino-snore ends in snore, which adds an n between the s and the vowel. The vowel sound that follows is close in both. Said quickly, the extra consonant is the only thing that separates the two words.
Coined in 1842
Wikipedia's article on dinosaurs says the English paleontologist Sir Richard Owen coined the word in 1842. It comes from Ancient Greek deinos, meaning terrible, potent or fearfully great, and sauros, meaning lizard or reptile. Owen used it for what he called a "distinct tribe or sub-order of Saurian Reptiles" then being recognized in England and around the world, as that article reports. It adds that Owen meant the name to evoke their size and majesty as well as their fearsome features, and it quotes his phrase "great fossil lizards".
Dinosaurs still around
By Wikipedia's account, scientists define dinosaurs as the group that includes the most recent common ancestor of Triceratops and modern birds, together with all of its descendants. By that definition birds are dinosaurs too, which means the riddle could be told, with a straight face, about a sleeping sparrow.
Variations to try
The same swap works whenever an animal name ends in a sound that matches a word for something done in sleep. A group can look for other pairs, and what does a snowman eat for breakfast is a fair next question.