Use double fold to cover/bind an edge, like a quilt. Use single fold for adding a casing to slip a string or a piece of elastic through.
When making a sleeveless dress, you can "bind" the edge with a contrasting doublefold tape (think lightweight cotton summer dress), or use singlefold tape as a narrow, light weight facing. When making a velvet dress, a self facing would be too bulky, so single fold tape is recommended for facings of this weight.
Hope this helps you think through other possible uses.