Musical theatre Cultre & theatre styles

Jukebox Musicals / Karaoke Musicals
I believe this is one of the more modern types of musical and does what it says on the tin – they are musicals where the audience is encouraged to join in with the songs.  I think one of the first musicals of this kind in the West End was (and is) Mamma Mia! Quite often they are centered around a well-known band or music recorded by a well-known band, for example, We Will Rock You is a jukebox musical which features many of the well known Queen songs.
Musical Drama
I expect most of the traditional / classical musicals feature in this category – they use music as another way of expressing emotion.  Characters will typically burst into song when the emotion of a scene is too much to be expressed using words alone.  They also tell a normally quite emotional story like the story of Billy Elliot where a young boy wants to pursue a career in dance but he lives in a time where men box – not dance.
Musical Comedy
This type of musical is for those who love to laugh (bet that surprised you), they generally have stories which lend themselves to comedy a bit like Avenue Q which for a start stars puppets and seeing them talk about it is a great comedy musical.  La Cage Aux Folles would be another good example.