keep one's nose to the grindstone vs plug away

keep one's nose to the grindstone and plug away both are verbs.

Word	Noun	Adjective	Verb	Adverb
keep one's nose to the grindstone	No	No	Yes	No
plug away	No	No	Yes	No

As verbs, keep one's nose to the grindstone and plug away are synonyms defined as:

keep one's nose to the grindstone and plug away: work doggedly or persistently

Other synonyms of keep one's nose to the grindstone include keep one's shoulder to the wheel, peg away, slog.

keep one's nose to the grindstone (verb)	plug away (verb)
work doggedly or persistently	persist in working hard
	work doggedly or persistently