Mules are official mint issue Roman coin that are hybrids, meaning they have the obverse of one emperor and the reverse of another. The numismatic term mule is derived from the animal mule, the hybrid offspring of a horse and a donkey, due to such a coin having two sides intended for different coins, much as a mule has parents of two different species. Coins of this type are generally scarce or rare. A modern day comparison would be a coin with the obverse (heads) of a US Penny and the reverse (tails) of a US Dime. Unofficial, ancient counterfeit or imitative, hybrids are very common and should not be described as mules. Curtis Clay explained on the Classical Numismatic Discussion Board:
"The term "hybrid" has become tainted in my mind, because so many of the coins so described in the earlier RIC volumes and in Roman Silver Coins are nothing but ancient counterfeits. Therefore I prefer to say "mule" for coins struck at the mint from mismatched official dies. The distinction official/unofficial is crucial. Official mules are for the most part very rare, and interesting as error coins and for showing a chronological connection between dies that we otherwise wouldn't have known were in use at the same time. Unofficial hybrids are very common and teach us nothing about the chronology of the official coinage."
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The Carpentum Mulare, or covered chariot, with two mules, is a type of consecration. [See Carpentum—Consecrativ—Thensa.] One of these with the epigraph S.P.Q.R. IVLIAE AVGVST., in honour of Livia, appears on a first brass of Tiberius.—A funeral biga of mules appears on large brass of Agrippina, wife of Germanicus; and of Domitilla, wife of Vespasian, with the word MEMORIAE preceeding their respective names.—The same type appears on a silver coin of Marciana, Trajan's sister, with the epigraph CONSECRATIO; and also on a first brass of Faustina senior.—A carpentum, drawn by two mules, appears on a rare first bras of Juia Titi, struck after her death, under the 15th consulate of Domitian, and which by the sacred title of DIVA prefixed to her name, proves that that princess had been placed by her "incestuous uncle" in the rank of divinities.—But we see other instances, as the intelligent author of Lecons de Numsmatique Romaine says, that "the car and pair of mules were not exclusively appropriated to designate consecrations."