Lyrical dance is a style of dance created by merging ballet and jazz. The style is usually danced at a faster pace than ballet but not as fast as jazz.
Jazz dance is the performance dance technique and style that emerged in America in the early twentieth century. Jazz dance began as an African American social dance that had roots in African slave dances.
Hip-hop dance refers to street dance styles primarily performed to hip-hop music or that have evolved as part of hip-hop culture.