Balayage
When you foil retouch, I know that you fold the foil in and close it around the sliced piece. But in the balayage method it appears that you simply let the foils just lie there. Thanks so much!
Common balayage application would involve using a powdered bleach lightening mixture to paint thin "highlights" all along the surface of the hair in order to create subtle highlights and draw attention to the surface of the hair.
However, since the term refers to a "free-form" application method, a variety of looks can be created. For example, imagine a hairstyle consisting of curly, layered hair where the tips of the layered curls are tinted in a dramatic color. This could be achieved by using a color brush to paint the ends of the hair without needing any additional tools.
The use of foil in a balayage method is likely simply a matter of the stylist's concern over color-bleed or dripping. Traditional balayage doesn't use foils and generally uses a tinting or lightening mixture that is thick enough to prevent the need for foil.
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See also:
How to dye hair
Advanced hair color techniques - Balayage
What is the difference between regular highlighting and a balayage?
Balayage under color technique to create a worn-out effect