why is this matrix in ref form and not rref?

question: what form is this matrix in?

$\displaystyle \left[ \begin{array}{cccc}

1 & 2 & 3 & 1 \\

0 & 1 & 2 & 3 \\

0 & 0 & 1 & -4 \\

0 & 0 & 0 & 0 \end{array} \right]

$

answer: row echelon form

confusion: the difference between rref and ref is that in ref it doesn't apply that "If a column contains a leading one, then all other enteries in that column are zero". So does that mean that the leading one is judging by the rows or columns it is in? For example in the second row there's a leading one with respect to the rows, but it's not the leading one in it's column.

sorry about the latex error, I can't figure out how to do matrices