peg away vs keep one's nose to the grindstone

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

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

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

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

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

peg away (verb)	keep one's nose to the grindstone (verb)
work doggedly or persistently	work doggedly or persistently