As a freelance teacher I can offer you different types of dance
Some examples are
Contemporary ( origins are drawn from Ballet technique but with more creative freedom and movement than pure classical Ballet)
Jazz/modern ( can be mixed but usually the style you would see in west end productions ie jazz hands) high leg kicks, over dramatic movements and exaggerations of steps.
Lyrical ( soft balletic style movements mimic the music)
Street ( popular style made even more famous by the BGT winners Diversity)
Freestyle ( set movements and steps which a dancer uses to freestyle to the music in competitions the music is not normally heard before hand so therefore the dancer has to freestyle these set moves to the music)
Freestyle movements sit in hand with Jazz / modern steps and a strong ballet technique foundation as there are leaps, spins and high leg kicks all that require a solid technique and skill to perform at a set standard.