Highlights and balayage both add lighter pieces to your hair. The difference is in how the colour is placed, and that changes how it grows out.
Highlights
Colour is applied in foils from the root, for an even, brighter result. Roots show sooner, so most people refresh them every 6 to 10 weeks.
Balayage
Colour is painted by hand, softer at the root and brighter towards the ends. It grows out gently, so many clients only come back every 3 to 4 months.
Your stylist will look at your base colour, your hair history and how much upkeep you want before recommending either. Always ask for a patch test before your first colour.