# Distinguishing between different notions of $R^2$

What is the distinction between

• $$R^2_{pop}$$ – the population R-squared
• $$R^2_{out}$$ – the out-of-sample R-squared
• $$R^2_{c.v.}$$ – the squared population cross-validity coefficient ?

These objects have been mentioned in earlier posts here, here and here.

I would appreciate an intuitive explanation. Ideally, some counter-examples would illustrate when the differences between these objects matter, and what goes wrong if one is used in place of another.