Let's sort out the differences in these two highlighting techniques:
* balayage
* slicing/weaving with foils.
Balayage is a freestyle colouring technique from France where the bleach or color is painted on
the hair in vertical stripes, and no foil is used. The color or bleach starts thin at the root and
gets heavier towards the bottom of the hair. This method saves oodles of time and lets your
stylist show his/her creative side. You can go as dramatic or as subtle as you want.
With Balayage there isn't a "root line", so I can go months between touch ups.
Here are some examples of Balayage:

Foiling is a control method so that the colored/bleached hair doesn't touch the rest of the hair.
Slices or weaved hair is placed inside the foil to process the bleach or color.
SLICING TECHNIQUE: A thin, 1/8 inch section of hair is taken with the end of a comb, painted, and
placed in foil. Results can look like this:

WEAVE TECHNIQUE: Probably the most popular highlighting technique. A thin section of hair is taken
and weaved through with the end of the comb, painted, and placed inside foils. The final result
can be like this:

Experienced, well educated hair colorists may use a mix of weaving and slicing, and balayage techniques on your
head.
Any highlighting technique can be good as long as you know what you want. First you just find a
photo that you want your hair to be like, then bring it into your hair stylist.
They'll choose the technique to get you there!
Enjoy a brighter you!
Trina