"Here am I" vs "here I am"

Is my understanding correct that here am I is just an archaic form of saying here I am? That is what Google seems to tell me.

Here am I is not always archaic: To express astonishment or disbelief, you can say "Here am I, a professor of physics, and you are telling me that gravity is caused by magnets!"

Or "Here are the apples that I said I would buy for you."

"Here" is an adverb. The phenomenon is called "Adverb Fronting Inversion"

Random Idea English at http://random-idea-english.blogspot.com/2014/09/exploring-inversion-and-fronting.html has a good explanation

Inversion and fronting

Inversion is often used in connection with fronting. Sometimes fronting involves inversion, often it doesn't. Sometimes that inversion is obligatory, sometimes it isn't.

• Fronting of a negative adverb, with obligatory inversion.

He had never seen such a wonderful sunset. (standard word order)

Never had he seen such a wonderful sunset. (fronted with inversion)

• Fronting of a prepositional phrase, with optional inversion A large dog lay in front of the fireplace. (standard word order)

In front of the fireplace, lay a large dog. (fronted with inversion)

In front of the fireplace, a large dog was chewing a bone. (fronted, no inversion)

• Fronting of wh-clause - here inversion is not possible

I've no idea why she's late. (standard word order)

Why she's late, I've no idea. (fronted, no inversion)

The commonest uses are “so do I” and “neither do I”.

The other instances are usually archaic (when this form was commoner) or poetic:

"Dearly did I love her"

"Eagerly will I go to the king's palace."