Full Idea
The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
Gist of Idea
There are 'particular' structures, and 'universal' structures (what the former have in common)
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
A Reaction
This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.