pencil box vs box

pencil box and box both are nouns.

Word	Noun	Adjective	Verb	Adverb
pencil box	Yes	No	No	No
box	Yes	No	Yes	No

As nouns, box is a hypernym of pencil box; that is, box is a word with a broader meaning than pencil box:

pencil box (noun)	box (noun)
a box for holding pencils	a blow with the hand (usually on the ear)
	a (usually rectangular) container; may have a lid
	separate partitioned area in a public place for a few people
	private area in a theater or grandstand where a small group can watch the performance
	the driver's seat on a coach
	any one of several designated areas on a ball field where the batter or catcher or coaches are positioned
	evergreen shrubs or small trees
	the quantity contained in a box
	a rectangular drawing
	a predicament from which a skillful or graceful escape is impossible