A more thorough search through the Maple TA Online Help has shed some more light on this question. Including the command randomize(): in Maple-based variable definitions sets the initial state of the random number generator using a number based on the system clock instead of the default seed in Maple.
Thus, using
$graphdisplay=plotmaple("randomize():GraphTheory[DrawGraph](GraphTheory[RandomGraphs][RandomDigraph]($n,$m)),plotoptions='width=512,height=512'");
$ans=maple("randomize():GraphTheory[AdjacencyMatrix](GraphTheory[RandomGraphs][RandomDigraph]($n,$m))");
would result in the two different random digraphs (which I do not want in this particular case).