It all began with macaroni. Our word pastiche is from French, but the French word was in turn borrowed from Italian, where the word is pasticcio. Pasticcio is what the Italians called a kind of "macaroni pie" (from the word pasta). English-speakers familiar with this multilayered dish had begun to apply the name to various sorts of potpourris or hodgepodges (musical, literary, or otherwise) by the 18th century. For over a hundred years English speakers were happy with pasticcio, until we discovered the French word pastiche sometime in the latter part of the 1800s. Although we still occasionally use pasticcio in its extended meaning, "pastiche" is now much more common.