And "kaşkol" in Turkish! I always assumed it was a word of Turkish origin. So interesting, thank you. :)
In English, a warm scarf is usually long and narrow and worn around the neck.
A shawl is big and often triangular (or a folded square) of heavy wool, worn over the shoulders, often instead of a jacket, nowadays mostly by women.
However a scarf can also be a much smaller square of thin cotton, silk, even wool usually folded in half and worn to cover hair, around neck (often indoors) or decoratively draped around neck or across shoulders.