The difference between Approximately and Nearly

When used as adverbs, approximately means imprecise but close to in quantity or amount, whereas nearly means with great scrutiny.

check bellow for the other definitions of Approximately and Nearly

Approximately as an adverb:

Imprecise but close to in quantity or amount.

Examples:

"In every box of matches there are approximately 40 matchsticks."

"Per 100g of chocolate there are approximately 11.6g of saturated fat."

"...approximately 60 beats per minute."

Nearly as an adverb (now, rare):

With great scrutiny; carefully.
Nearly as an adverb:

With close relation; intimately.
Nearly as an adverb:

Closely, in close proximity.
Nearly as an adverb:

In close approximation; almost, virtually.

Examples:

"He left a nearly full beer on the bar."

"I nearly didn't go to work yesterday."
Nearly as an adverb:

Stingily.