With an indexed shifter, each gear change moves a fixed amount of cable. The rear derailer is supposed to move a certain distance (the distance between cogs) for each fixed amount of cable pulled.
There is the fact about some sram levers not working with shimano shifters and vice-versa, and that's because each brand works with a different amount of cable pull per shift.
If you have a friction shifter, you can pull any amount you want, so you'll always be able to get the right derailer position for a given gear (of course, given your shifter covers the required range), and in this case you could use any suitable derailer.
So, the distinction you mention has to do with compatibility between a given derailer and a given indexed shifter. If you match them wrong, shifting would be very disfunctional (I've seen it happen).
Besides that, it would be theoretically possible to use a non-indexed derailer with a given indexed shifter, but only if they happen to have the same cable-displacement-to-lateral-displacement ratio.