What is the difference between identity and equality in OOP?

Identical vs. Equal objects

Two objects are said to have identical states (deep equality) if the graphs representing their states are identical in every respect, including the OIDs at every level.

Two objects are said to have equal states (shallow equality) if the graphs representing their states are same, including all the corresponding atomic values. However, some corresponding internal nodes in the two graphs may have objects with different OIDs. Example: This example illustrates the difference between the two definitions for comparing object states for equality.

o2 = (i 2 , tuple, <a 1 :i 5 , a 2 :i 6 >)
o3 = (i 3 , tuple, <a 1 :i 4 , a 2 :i 6 >)
o4 = (i 4 , atom, 10)
o5 = (i 5 , atom, 10)
o6 = (i 6 , atom, 20)

In this example, the objects o1 and o2 have equal states (shallow equality), since their states at the atomic level are the same but the values are reached through distinct objects o 4 and o 5 .

However, the objects o1 and o3 have identical states (deep equality), even though the objects themselves are not because they have distinct OIDs. Similarly, although the states of o4 and o5 are identical, the actual objects o4 and o5 are equal but not identical, because they have distinct OIDs.

To add, identity is also known as referential check (references to objects, get it?) and equality as structural check by some authors. At the end of the day an object in memory abstract is just a map/table structure indexed at certain memory address. There can be one or many references (memory addresses) pointing to it. They all are referential-ly identical. When contents of same object is copied to another counterpart then both are structurally equal.