cutwork vs fancywork

cutwork and fancywork both are nouns.

Word	Noun	Adjective	Verb	Adverb
cutwork	Yes	No	No	No
fancywork	Yes	No	No	No

As nouns, fancywork is a hypernym of cutwork; that is, fancywork is a word with a broader meaning than cutwork:

cutwork: embroidery in which the design is outlined in a buttonhole stitch and the intervening material is cut away
fancywork: decorative needlework

Other hypernyms of cutwork include embroidery.

cutwork (noun)	fancywork (noun)
embroidery in which the design is outlined in a buttonhole stitch and the intervening material is cut away	decorative needlework