What is the running of the bulls called in Spain?

In Catalonia, it is a 'correbou'. Google the word and have a look.

In Pamplona, where the most famous bull run is held, the actual running of the bulls is called in Spanish El Encierro and is part of the San Fermin festival.

Encierro, from the verb "encerrar", to lock/shut up, to pen). Running of the Bulls is literally translated into "Corrida de Toros" but this term is specifically used for the bullfighting events not for the being chased by bulls on the street event. Toro is bull. This is why the animal that represents Taurus is a bull. Taurus (latin) for bull.Bullfighting is also called tauromachy but this term is rarely used.