Part of a noun or an adjective

It all depends on HOW this word is used IN A SENTENCE.

You cannot take one word out of context and expect to come up with a definition or its part of speech.

Well, as I'm writing a definition, I can't exactly use a sentence, but I think I see your point. So to clarify, here are the two contexts I'm looking at.

intrinsic (adj.) = essentially part of something
intrinsic (adj.) = essential part of something

I don't like the second definition, because the word "part" is being use as a noun, and I am defining an adjective.
So in the first definition, I am curious to know whether the word "part" or the phrase "part of" is being used incorrectly, and if not, how would you explain its use?

Maybe this will help you:

essential = adjective
essentially = adverb