Cartoonist and illustrator Thomas Nast (1840-1902) popularized both symbols but invented only one of them.
Democrat Andrew Jackson first used the donkey as a symbol for his party after his opponents in the 1828 presidential election called him a “jackass”; Nast’s cartoons later helped to make the symbol famous.
Nast himself introduced the Republican elephant in an 1874 cartoon.
At first, the elephant was only meant to symbolize the overwhelming strength of “the Republican Vote”; it soon came to stand for the Republican party as a whole.