What is the relationship between gravity and inertia?

Einstein told us that gravity and inertia are identical.

Yes, Einstein did say that gravity and inertia are identical, despite people in the comments telling you to the contrary. This is a common error derived partly by Einstein’s equating of gravitational mass with inertial mass (in his principle of equivalence), but mostly simply because gravity and acceleration look like different phenomenon.

You could say that gravity and inertia are identical, and that the gravitational field and acceleration are inductive pairs (similar to the electromagnetic field and electric current.) A gravitational field induces acceleration, and acceleration induces a gravitational field.

From Einstein’s 1918 paper: On the Foundations of the General Theory of Relativity… http://einsteinpapers.press.princeton.edu/vol7-trans/49

“Inertia and gravity are phenomena identical in nature.” - Albert Einstein

In a letter Einstein wrote in reply to Reichenbacher... .http://einsteinpapers.press.princeton.edu/vol7-trans/220

“I now turn to the objections against the relativistic theory of the gravitational field. Here, Herr Reichenbacher first of all forgets the decisive argument, namely, that the numerical equality of inertial and gravitational mass must be traced to an equality of essence. It is well known that the principle of equivalence accomplishes just that. He (like Herr Kottler) raises the objection against the principle of equivalence that gravitational fields for finite space-time domains in general cannot be transformed away. He fails to see that this is of no importance whatsoever. What is important is only that one is justified at any instant and at will (depending upon the choice of a system of reference) to explain the mechanical behavior of a material point either by gravitation or by inertia. More is not needed; to achieve the essential equivalence of inertia and gravitation it is not necessary that the mechanical behavior of two or more masses must be explainable as a mere effect of inertia by the same choice of coordinates. After all, nobody denies, for example, that the theory of special relativity does justice to the nature of uniform motion, even though it cannot transform all acceleration-free bodies together to a state of rest by one and the same choice of coordinates.” - Albert Einstein

From Albert Einstein’s book: The Meaning of Relativity, pg 58

“…In fact, through this conception we arrive at the unity of the nature of inertia and gravitation. For according to our way of looking at it, the same masses may appear to be either under the action of inertia alone (with respect to K) or under the combined action of inertia and gravitation (with respect to K’). The possibility of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical mechanics, that all the difficulties encountered must be considered as small in comparison with the progress.” - Albert Einstein

Here and in other places Einstein specifically emphasizes the equivalence of gravity and inertia, and not merely the equivalence of gravitational and inertial mass.

… But is this where we are left hanging: that gravity and inertia are both identical and equal? Is gravity inertia? Or is inertia gravity?

Yes, that is kind of where we are left hanging.

What is the next step beyond saying that gravity and inertia are both identical and equal?

The next step would be in solving in greater detail the physics of inertia. You can search for things like “source of inertia” to get an idea of how some physicists in the past have approached this problem. My feeling is that when the mystery of inertia is more or less solved, Einstein’s assertion on the equivalence of gravity and inertia will be validated.