Intimation vs Notify - What's the difference?

As a noun intimation

is the act of intimating; also, the thing intimated.

to give (someone) notice of (something).

(en noun)

The act of intimating; also, the thing intimated.

Announcement; declaration.

* (Holland)

They made an edict with an intimation that whosoever killed a stork, should be banished.

A hint; an obscure or indirect suggestion or notice; a remote or ambiguous reference; as, he had given only intimations of his design.

Without mentioning the king of England, or giving the least intimation that he was sent by him.

* 1862 , (Henry David Thoreau), :

At length, perchance, the immaterial heaven will appear as much higher to the American mind, and the intimations that star it as much brighter.

(en-verb)

To give (someone) notice of (something).

* apprise * inform