A nursery rhyme is a traditional poem or song for children in Britain and many other countries, but usage of the term dates only from the late 18th/early 19th century. The term Mother Goose rhymes is interchangeable with nursery rhymes.
Illustration of "Hey Diddle Diddle", a well-known nursery rhyme
Popular Nursery Tales and Rhymes, Warner & Routledge, London, c. 1859
"Baa, Baa, Black Sheep", from a 1901 illustration by William Wallace Denslow
Mother Goose is a character that originated in children's fiction, as the imaginary author of a collection of French fairy tales and later of English nursery rhymes. She also appeared in a song, the first stanza of which often functions now as a nursery rhyme. The character also appears in a pantomime tracing its roots to 1806.
The opening verse of "Old Mother Goose and the Golden Egg", from an 1860s chapbook
Mary Goose's gravestone in Granary Burying Ground in Boston, Massachusetts
Frontispiece from the only known copy of the first English translation, 1729
Joseph Grimaldi (right) in the "favourite pantomime of Mother Goose"