Are there different types or styles of ocarinas?
Yes, there are many different types. Some are shaped like animals, some are transverse, like a flute or fife, others, you blow straight into like a clarinet, and they generally have anywhere from 4 to 12 toneholes. Again, there’s more latitude in the design of vessel flutes than there is for tubular flutes.
(History of the Ocarina)
(Making an Exceptional Ocarina)
Other Links: Karl's Ocarinas
General Ocarina Information