What is the difference between equality and logical identity? I'm reading the book Introduction to Logic and to the Methodology of the Deductive Sciences by Alfred Tarski and he states:
"In this book we consider the notion of equality among numbers always as a special case of the general concept of logical identity. One should add, however, that there have been mathematicians who —as opposed to the standpoint adopted here— did not identify the symbol "=" occurring in arithmetic with the symbol of logical identity; they did not consider equal numbers to be necessarily identical, and therefore looked upon the notion of equality among numbers as a specifically arithmetical concept."
So what is the difference between "=" and "logical identity"?

I expect that Tarski means by "logical identity" something close to "literally the same thing", which could be applied to numbers in arithmetic, sets in set theory, or anything else. 
Now imagine a mathematician X (not Tarski) who might say something like "a rational number is a pair of integers called numerator and denominator", so that "2/4" and "1/2" are different "rational numbers" because they have different numerators and denominators. Then X would still write "2/4=1/2" (they're a mathematician, after all), but might say the reason is that the criteria for rational numbers "a/b" and "c/d" to be equal in the sense of "=" is the arithmetic property that  $a*d=b*c$ (for whatever equality means for integers).
Tarski is saying "I'm not doing that mathematician X stuff. There's no arithmetic in my intended meaning of '='."
