Full Idea
Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system.
Gist of Idea
Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system
Source
Peter Smith (Intro to Gödel's Theorems [2007], 04.7)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.36