sugar vs cane sugar

sugar and cane sugar both are nouns.

Word	Noun	Adjective	Verb	Adverb
sugar	Yes	No	Yes	No
cane sugar	Yes	No	No	No

As nouns, cane sugar is a hyponym of sugar; that is, cane sugar is a word with a more specific, narrower meaning than sugar:

sugar: a white crystalline carbohydrate used as a sweetener and preservative
cane sugar: sugar from sugarcane used as sweetening agent

As nouns, cane sugar is a hyponym of sugar; that is, cane sugar is a word with a more specific, narrower meaning than sugar:

sugar: an essential structural component of living cells and source of energy for animals; includes simple sugars with small molecules as well as macromolecular substances; are classified according to the number of monosaccharide groups they contain
cane sugar: sucrose obtained from sugar cane

sugar (noun)	cane sugar (noun)
a white crystalline carbohydrate used as a sweetener and preservative	sugar from sugarcane used as sweetening agent
informal terms for money	sucrose obtained from sugar cane
an essential structural component of living cells and source of energy for animals; includes simple sugars with small molecules as well as macromolecular substances; are classified according to the number of monosaccharide groups they contain

sugar (verb)	cane sugar (verb)
sweeten with sugar