Unicode defines equivalence relations, yes. But nowhere does is a program that uses Unicode required to use a equivalence relation whenever it wishes to compare two strings. It probably should use one, but there are various reasons why it might want strict equality for certain operations.
(OK, so "required" might be overstating it; you are perfectly free to write a program that doesn't conform to the standard. But most people will consider that a bug unless there is a good reason for it)