Which came first, the old lady or the scarf?

Today on the bus there were at least 3-4 babushkas (Russian word for grandma).

How to recognize a babushka:

old.

lady.

practical shoes.

thick ankles.

long winter coat (at least 54 years old. the coat).

and of course, a scarf on the head.

Some call a scarf worn on the head a babushka.

So here's the question:

Which came first?

Do they call the old lady "babushka" because she wears the scarf on her head?

Or do they call the scarf "babushka" because all babushkas wear them?

It's like the chicken and the egg question.

Although, if you know anything, you know the chicken came first.

In case I didn't paint a good enough picture for you: (as found in a google image search)