lace vs shoelace

lace and shoelace both are nouns.

Word	Noun	Adjective	Verb	Adverb
lace	Yes	No	Yes	No
shoelace	Yes	No	No	No

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

lace: a cord that is drawn through eyelets or around hooks in order to draw together two edges (as of a shoe or garment)
shoelace: a lace used for fastening shoes

Other hyponyms of lace include bootlace, shoe lace, shoe string, shoestring.

lace (noun)	shoelace (noun)
a delicate decorative fabric woven in an open web of symmetrical patterns	a lace used for fastening shoes
a cord that is drawn through eyelets or around hooks in order to draw together two edges (as of a shoe or garment)

lace (verb)	shoelace (verb)
add alcohol to (beverages)
draw through eyes or holes
spin, wind, or twist together
do lacework
make by braiding or interlacing