I've seen people make a distinction between a derailleur being for friction or indexed.
Is this distinction somehow functional? I can't see how it could be, because every derailleur I've ever seen just takes a movement in the cable and translates it into a movement in the cage.
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.
With the possible exception of the newer electromechanical shifting systems, the derailleurs themselves are not "indexed"; they move within a range according to the cable movement. The shifters control the cable movement, and are the thing that are indexed — not the derailleurs.
Most likely what people are referring to is whether the derailleurs are part of a part of a group that uses indexed shifting. But assuming the same high-low range, take-up capacity (for a rear derailleur) and cable pull ratio, a derailleur that was originally part of a friction-shifting group should be interchangeable with an indexed shifting group and vice-versa.
Expanding on djangodude's comment, rear drive train groups (derailleur, cassette, chain, shifter) tend to be more sensitive to derailleur alignment. They also tend to be designed to work together. Various pins and ramps on the cassette exist to encourage the chain to shift up or down as necessary. For a chosen gear, the derailleur "sweet spot" -- the position where the chain flows smoothly & quietly without trying to jump up or down a gear -- is narrower in an indexed group.
That said, you can certainly use an indexed group with friction shifters, but your shifting must be much more precise.
