First, “nature” (Greek: physis, Latin: natura) denotes what something is—the set of essential properties and capacities that make a being what it is and not something else.
Ok. Noted.
“Essence” (Greek: ousia, Latin: essentia or substantia) is closely related, often interchangeable, but with a subtle distinction: essence is that by which a thing is what it is; it is “that which makes a thing to be what it is.”
Alright. So it sounds to me like you are saying a "nature" is a descriptive set of attributes. This set of necessary attributes confirms the "essence" of the being. But why is "essence" anything more than the set of attributes? Part of this is a categorical description too. The term "human" is a category. Anything fitting into that category would have the "nature" of "human". But it seems "essence" is pretty much the same thing.
In concrete terms, the "nature" of a human is to be a rational animal; the "essence" is the underlying reality that actualizes this nature.
Ok, good. An example.
Humans have a whole host of characteristics, but most are shared. Like "two legs". This is common for "human" but doesn't really define "human". After all, a legless human is still a human. So the defining set of characteristics is a set : { animal, rational }. How rational? Would a mentally handicapped human cease to be human? Is a human fetus (not capable of meaningful rationality) not really "human"?
What does it mean to "actualize" a nature, other than display the necessary set of attributes that cause you to fit into the category?
In the case of God, nature and essence refer to the one, undivided, eternal act of existence—pure actuality (actus purus)—which is to be itself: Ipsum Esse Subsistens, Subsistent Being Itself, as Aquinas says.
Ok. But this is way too abstract for me at the moment.
I need more concrete examples. Do dogs have a "nature"? Do cats? What separates them? Do poems have a nature?