ink vs fill up

ink is a noun but fill up is not a noun.

Word	Noun	Adjective	Verb	Adverb
ink	Yes	No	Yes	No
fill up	No	No	Yes	No

As verbs, fill up is a hypernym of ink; that is, fill up is a word with a broader meaning than ink:

Other hypernyms of ink include fill, make full.

ink (noun)	fill up (noun)
dark protective fluid ejected into the water by cuttlefish and other cephalopods
a liquid used for printing or writing or drawing

ink (verb)	fill up (verb)
fill with ink	make full, also in a metaphorical sense
mark, coat, cover, or stain with ink	become full
append one's signature to	eat until one is sated
	fill or stop up