When hitting "D" to draw the current selection, the macro recorder records:

    run("Draw");

When you use 'Edit > Draw' instead, you get a "Process stack?" dialog, and after selecting "No", the recorded command is:

    run("Draw", "slice");


The keyboard shortcut should record the same command as the menu command, as is the case for the 'Fill' command, where both 'F' and 'Edit > Fill' will record:

    run("Fill", "slice");


See also this post on stackoverflow.com:
http://stackoverflow.com/q/33715555/1919049