slog vs keep one's nose to the grindstone

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

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

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

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

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

slog (verb)	keep one's nose to the grindstone (verb)
strike heavily, especially with the fist or a bat	work doggedly or persistently
walk heavily and firmly, as when weary, or through mud
work doggedly or persistently