Two things are called the style, and they do unrelated jobs.

 

The accompaniment style is what the band plays. Choose it from the player controls. There are 50 built in, across Jazz, Latin and Pop, with Blues, Brazilian and Salsa available as an in-app purchase. A style you pick by hand stays with that song, and a playlist remembers the style, tempo, repeats and key of each of its songs separately (see Song settings).

 

The style indicator is only text, shown at the top left of the chart, and you edit it in Song Info like the composer's name. When you save, iReal Pro reads it and selects the closest accompaniment style it can find, so 'Ballad' selects Jazz - Ballad. After that the two are independent. Sorting the song list by style sorts on this text, not on the band.

 

For the full guide, see Accompaniment styles on the iReal Pro website.