The difference between Naturally and Normally

When used as adverbs, naturally means in a natural manner, whereas normally means under normal conditions or circumstances.

check bellow for the other definitions of Naturally and Normally

Naturally as an adverb:

In a natural manner.

Examples:

"Although he was unused to the situation, he tried to act naturally."
Naturally as an adverb:

Inherently or by nature.

Examples:

"Boys are naturally aggressive."
Naturally as an adverb:

Surely or without any doubt.

Examples:

"I shall naturally protest at that decision."

Normally as an adverb:

Under normal conditions or circumstances; usually; most of the time

Examples:

"Normally, I eat breakfast at 6am, but today, I got up late and didn't eat until 9."
Normally as an adverb:

In the expected or customary manner.

Examples:

"Lisa ate normally, until she realised that she was late for [[choir]], when she sped up."
Normally as an adverb:

To a usual or customary extent or degree.

Examples:

"He was abnormally agitated, she only normally so."
Normally as an adverb (mathematics, statistics):

In the manner of a variable with a Gaussian distribution.