I have a quick question regarding the difference between echelon form and reduced row echelon form (rref). According to my googling these seem to be the same, but to me it seems that the difference between the two is that echelon form only requires the first value of the first row to be 1. The first non-zero value of each row after the first one can be any value as long as it's not 0.
As for reduced row echelon form every first non-zero value of a row has to be 1.
Am I correct with this or am I completely mixing things up? If I'm correct, when would the echelon form be fine and when do I have to use RREF?