$(3, 2)$ is the coordinate vector of $(3, 2) \in \reals^2$, relative to the standard basis

Terms

Term	This example	Why
vector	✓	$(3, 2)$ is a vector in $\reals^2$, because it is an element of the vector space $\reals^2$.
coordinate vector	✓	$(3, 2)$ is its own coordinate vector relative to the standard basis, because $(3, 2) = 3 (1, 0) + 2 (0, 1)$.

Vector vs. coordinate vector: In $\reals^n$ with the standard basis, a vector is its own coordinate vector, which is why vectors and coordinate vectors are easy to confuse.