True ... "cellulose" is a broad term and can consist of many things. But if I recall correctly, most "cellulose" filter media is typically made of wood products. Never heard or read of any oil filter cellulose media being made of cotton, but maybe it's possible.
I concur. Cellulose is a plant fiber based product. Wood based cellulose is likely the most common type for oil filters but I suspect that a blend of wood, cotton and perhaps other plant based cellulose are used to make the media.