The second meaning of "identical" is qualitatively identical. X and Y are qualitatively identical if and only if X and Y have exactly the same properties. That is, every property of X is a property of Y, and every property of Y is a property of X. In this sense of "identical", qualitatively identical, it is possible for two things to be identical.
If X and Y have exactly
the same properties, how can they be two things rather than one? In other words, how can they be qualitatively identical without being numerically identical?
Leibniz's Law of Identity holds that necessarily, if X = (is identical) Y, then every property of X is a property of Y, and conversely, every property of Y is a property of X. This Law is pretty well accepted as the definition of numerical identity. And has the name of of "the indiscernibility of identicals. The question you are asking is about the converse of the indiscernibility of identicals, namely, the identity of indiscernibles . Which is whether necessarily, if every property of X is a property of Y, and every property of Y is a property of X, then X and Y are identical. Now this is more controversial. Leibniz held that this principle was also true. But, if it is true, it is not intuitively true as the first principle is. After all, why could there not (to use Leibniz's example) be two (numerically two) different leaves which happened to have the very same properties? There are just two of them. Leibniz himself, although believing that the principle of the identity of indiscernibles was also true, did not think that it was self-evidently true as he thought that the converse principle, the indiscernibility of identicals, was self-evidently true. He thought it was true, but for metaphysical reasons such as that a rational God would not created two qualitatively identical leaves, since He would have no reason to do so. And, if He did, he would have no reason to place one in one place and the other in a different place. But the point is that there are two different principles: 1. If two things have all their qualities in common, then there are really not two things but just one thing under two different names. And, 2. that if there are 2 things with all their qualities in common, then there are not really 2 things, but just 1 thing. The principles are converses of one another (and so, not the same principle). And 1. is intuitively true, but 2, if true, not intuitively true.