Latin was a style of Earth music that originated from the Latin culture.
Mariachi is a type of music with a uptempo Latin beat; whereas the Spanish guitar is more of a gentle Latin beat. In order to pass the time while en route to Risa in the type 15 shuttlepod Onizuka, Geordi La Forge listened to a piece of Latin music played by a Spanish guitar. (TNG: "The Mind's Eye")
The mambo is also a type of Latin dance music. Jean-Luc Picard requested such music while the USS Enterprise-E visited Ba'ku in 2375. (Star Trek: Insurrection)