Full Idea
There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
Gist of Idea
There are Formalist, Relativist, Universalist and Pattern structuralism
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
A Reaction
I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?