Leibniz's law

As we discussed in class, Leibniz's law states that if A and B are the same thing, then any property of A must also be a property of B. This makes complete sense because if two things are identical, they share all their properties in common and conversely, and if two things share all their properties in common, then they are identical. According to the indiscernibility of identicals,if two things are identical, then no difference between them is discernible, and according to the identity of discernible, if no difference is discernible between two things, then they are identical.
It may, however, be worth noting that two things may be similar to, or the same as, each other in possessing many distinct kinds of properties. Identity between two things may involve material, formal, spatial, temporal, relational, and other kinds of properties.

Can an exact duplicate or replica of something be properly called "identical to" or "the same as" that thing? If so, why may there still be some doubt or uncertainty about whether the two things are alike in every respect? What may happen to the identity of the two things as they change over a period of time?

Surely, there must be some properties that are relevant to sameness, and some that are irrelevant. Should we then relativize or qualify the indiscernibility of identicals by saying that in order for two things to be the same, they must share all properties that are essential or relevant to their sameness? Some properties may be essential to the identity of two things, while other properties may be unessential.