I know for sure that cotton can describe objects such as cotton clothes, cotton field, or cotton seed. However, I have a few questions.
1: Can cotton refer to the soft, gathered, and fluffy state of cotton such as cotton of comforters, the infill ?
2: Can cotton refer to the general idea of something soft, gathered, white, and fluffy, but not necessary to be cotton? For example, the nylon infill in a comforter.
Cotton used for filling or lining quilts is called batting or (more precisely) cotton batting. From Merriam-Webster's Eleventh Collegiate Dictionary (2003):
batting n ... 2 : layers or sheets of raw cotton or wool or of synthetic fibrous material used for lining quilts or for stuffing or packaging; ...
As that definition indicates, you can use batting (but not cotton batting) to refer to non-cotton infill of the types you describe.
1: Sure, if it's cotton, you can call it cotton.
2: No, if it's not cotton, you ought not to call it cotton, unless perhaps you mean to be metaphoric ("The cotton of the clouds billowed up in the East"). Perhaps you could say it's cottony, or cotton-like.
In the US, the filling fluffy stuff is called, as Sven Yargs pointed out, "batting" or "cotton batting".
In the UK, it's more likely to be called "cotton wool", or "stuffing".
However, you can use the word cotton to mean any form of cotton you like. It's just, whether it would be the first form that someone would think of depends on context. "She filled her teddy with cotton" might not make one think of batting. "She dug her hands in the light fluffy cotton", does.
The form of batting does get a reference in the US term "Cotton candy".
Cotton refers to the material itself, not that the material is soft and fluffy. You could call a comforter made out of cotton a "cotton comforter", but you would again be referring to the material. If the comforter were instead made out of nylon, you could say that it's "like cotton" to get your point across.
