Balayage is a freehand technique whereby the colourist paints your hair with a brush as if it were a canvas and applies highlights (or lowlights) selectively to give the hair a more natural sun kissed look, particularly framing the face, for instance. Foil sheets are only applied to separate the sections rather than wrap the colour.
It's not easy to do well without proper training and a lot of practice, as you've sadly discovered.
Ombré is the term for colour that blends from dark to light. (Reverse ombré is light to dark)
I think you need to ask for a refund and go elsewhere for it to be fixed. What you have looks nothing like the picture you've attached and appears to have been done by someone who doesn't have a clue. The lighter pieces are brassy and start far too high on the head.