Definition:Orthogonal Latin Squares

Definition
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\mathbf A$ and $\mathbf B$ be Latin squares of order $n$.

Let $\left[{a}\right]_{i j}$ and $\left[{b}\right]_{i j}$ be the elements of $\mathbf A$ and $\mathbf B$ respectively whose indices are $i$ and $j$.

Then $\mathbf A$ and $\mathbf B$ are orthogonal :
 * for all $i$ and $j$, the ordered pairs $\left({\left[{a}\right]_{i j}, \left[{b}\right]_{i j}}\right)$ are distinct.

That is, $\left({\left[{a}\right]_{i j}, \left[{b}\right]_{i j}}\right)$ appears no more than once for every ordered pair $\left({i, j}\right)$.

Also known as
Some sources use the term mutually orthogonal where just orthogonal will do.

While this is clumsy (mutual orthogonality is defined on a set, usually greater than $2$ in size), it is not inaccurate.