[JUSTIFY]They both mean the same thing as far as I can tell. I think this may be a language problem, the first form might be more natural in english whereas the other sounds more natural in other languages (for instance french).[/JUSTIFY]
Like others said the variable names can be whatever you want to use, but standard convention is that a matrix of size $m \times n$ corresponds to a linear system of equations, which means that there are $m$ rows and $n$ columns. That corresponds to $m$ equations and $n$ variables.