cobweb vs spider's web

cobweb and spider's web both are nouns.

Word	Noun	Adjective	Verb	Adverb
cobweb	Yes	No	No	No
spider's web	Yes	No	No	No

As nouns, spider's web is a hypernym of cobweb; that is, spider's web is a word with a broader meaning than cobweb:

cobweb: a dense elaborate spider web that is more efficient than the orb web
spider's web: a web spun by spiders to trap insect prey

Other hypernyms of cobweb include spider web.

cobweb (noun)	spider's web (noun)
a dense elaborate spider web that is more efficient than the orb web	a web spun by spiders to trap insect prey
filaments from a web that was spun by a spider	a web resembling the webs spun by spiders
a fabric so delicate and transparent as to resemble a web of a spider