This is a question about terminology. I hope it is not too silly but I haven't been able to find a clear answer. Basically, is there a more or less standard name for a function from an n-dimensional space into another n-dimensional space that maps each coordinate independently?
In formal terms, let's suppose we have two sets $A$ and $B$ and we can define functions mapping one set to the other $f \colon A \to B$. If, for an integer $n > 1$ we take the Cartesian products $A^n$ and $B^n$, then we can define functions $g \colon A^n \to B^n$. One simple form of such a function would be $$g(a_1, \dots, a_n) = (f_1(a_1), \dots, f_n(a_n)),$$ where each $f_i$ is a function from $A$ to $B$. But of course there will also be more general $g$ functions that don't map each coordinate independently. I'm looking for the English words that express this distinction as in $g$ is a 'whatever' function vs $g$ is a 'non-whatever' function.
I am aware of certain particular cases, like the diagonal vs non-diagonal linear maps in a vector space. But I'm wondering if there are any standard names for this distinction in the general case where we simply have sets, Cartesian products, and functions.