In terms of practical reasoning, what are the constraints/conditions where one can infer that (putatively) two things are not identical on the basis of them seeming to have different properties?
At first read this might seem odd, but consider the story of the blind men and the elephant: One day, an elephant is brought to town. The six blind men of the town, never having encountered one before, go to it. The first, at its trunk, declares "It is like a snake!", the second at the tusk declares "It is like a spear!", the third, at its ear declares "It is like a fan!", the fourth, at its leg declares "It is like a column!", the fifth, at its side declares "It is like a wall!" and the fifth, touching just the tip of its tail declares "It is like a mouse!".
One place where this comes up is in Descartes' Meditation -- he infers that mind and body are distinct, but he could just be a blind man who touched the elephant in two different places and declared that it must be two things. It seems like one needs additional assumptions/constraints to make this leap.
I prefer to use natural(ish) language, so let "all properties same" indicate the formal statement "for a given x,y, for all properties p, x has p iff y has p" (or however you'd like to more formally state it). Leibniz's law is usually stated "if 'all properties same for x,y' then 'x,y are identical'". Implication from the properties from the identity. However, the converse implication is (seems?) obviously true: "if 'x,y are identical' then 'all properties are the same'". Thus the relationship is one of bidirectional implication. Therefore you should be able to infer "different properties therefore not identical", but it's not clear to me that you can make this inference in general; hence the need for additional constraints.