Difference: Scarf // Loop // Neck Warmer // Cowl?

Dear users, dear designers,
you can wrap a loop around your neck multiple times, but it is closed and not open like a scarf. If the loop includes a twist, then it is a Möbius. If the scarf cannot be wrapped around the neck multiple times, then is it a neck warmer or cowl?
Have I understood all of that correctly?

I'm only asking because I just found this pattern in the shop.

Sew a Quick Neck Warmer

I’d venture to say that a loop and a circular scarf are the same thing—namely, a closed scarf, a scarf with no end. In English, it’s often called an “infinity scarf.”

A slip-on scarf is actually often a scarf that’s pulled directly over the head without wrapping it around, and fits snugly right away. This type of scarf is also called a tube scarf.

The Möbius is a “twisted” loop—exactly :) If you hold one of these in your hands for the first time and don’t know that, the twist can drive you to despair because you might think the scarf is folded wrong somehow. But that’s how it’s supposed to be, and it looks great! :) 

OK, thanks for the info. I thought a loop would have enough fabric for multiple wraps?

I found another term here that fits.
I like “neck sock.”

Sewing pattern ☆ Reversible Neck Sock