I've used bit reduction and ring modulation only rarely, but I've played around with them a lot. When I do use one of these effects, I find their sound mangling results to be similar. Am I missing some obvious use of one or the other? Any artistic examples of using them (aside from trying to make samples sound more "sampled")?

Maybe I should add that I don't have a lot of experience with ring modulators in general. But I find that with, say, MRingModulator I am able to get all of the same effects as with any bit crusher I've used. But that it's such a specifically gritty sound...I guess I'm looking for either inspiration or elucidation.

Ring modulators, which have been around since Moog Modular days, are used for inharmonic compound sounds, such as bell tones. Sometimes they're used for nasty electronic percussion. Beyond that, I don't know what they're good for.
 
The only similarity between ring modulators and bit crushers is that both introduce inharmonic components. But whereas a ring modulator derives new tones from the sum and difference frequencies of two combined tones,  a bit-reducer's added frequency content is mostly uncorrelated quantization noise, and as such is largely unrelated to the source spectrum. 
 
I have never found a use for wordlength reduction as a sound-sculpting tool. Hurts my ears.

Bit reduction is an effect like any other, and has its uses in certain genres. You probably wouldn't want to use it on a folk track, for instance. But it can sound great in other scenarios. For instance it's a popular technique to get that fat, crunchy sound that came from the early 12-bit Akai samplers in hip hop. And the old 8-bit video game music had a particular sound which some people find nostalgic. Personally a big part of mixing to me is in creating contrasts, for instance the contrast between dull sounds and bright sounds, between dry sounds and reverbed sounds, clean sounds and distorted sounds etc. Bit reduction is another tool in that palette. Not something you'd want to throw your whole mix through but it can sound great on a select instrument in the mix, not necessarily throughout the whole song. 
 
Ring modulation is the same thing, a nice bit of tonal interest which can work well in certain situations but you wouldn't really want to base an entire track around it. You can get ring modulator guitar pedals, great for a bit of select nastiness in certain parts of the song. Creating contrast again. I'm no expert in ring modulation but isn't one of its characteristics that it has a pitch aspect to it? Whereas bit reduction is just squaring off waveforms. Geist has both bit reduction and ring modulation as part of its distortion section but I don't think I've ever managed to get the same sound from the ring modulator as I have from the bit cruncher. Both add distortion and grit but not in the same way. 

Ring modulation is quite different to bit-crushing/sample bit reduction. The process pre-dates synths, it was invented in the 1930s and used to frequency multiplyphone calls so the same line could carry many calls. It was found on at least one instrument by the late 1940s. Ring modulation is a form of "frequency mixing", and it works, put very simply, like this.

Ring modulation takes two input signals and outputs the sum and difference of those two frequencies. As an example, let's take two frequencies, say 3,000Hz and 2,000Hz. Passed through a ring modulator the output would be the sum of the frequencies = 5,000Hz and the difference between them = 1,000Hz. To get deeper into the workings involves some serious maths, but the key thing is that if the two frequencies are harmonically related, e.g. an octave apart, then the generated harmonics will also be related to those frequencies and the result is changed in tone but still musical.

If the two inputs are not harmonically closely related then you get something else :-)

It's used quite a lot to produce metallic sounds, or the perception of two or more notes that move away from or towards each other or "beating" between two or more frequencies.

The same frequency mixer concept is used in old-fashioned guitar octave fuzzes where a single note produces an octave up (or sometimes down) sound as the note pitch is doubled (or halved) but a variety of glitches and harmonic/inharmonic sounds if chords are played. Octave fuzzes actually aren't ring modulators, but a different variety of frequency multiplier/divider that has some of the same chatacteristics.

There's a good short demonstration of Electo-Harmonix's ring modulator, which explains it all much better than I can, here - https://www.youtube.com/w...ist=PL4690E06660453640

It's called "ring modulation", in case anyone's wondering, because the original circuit used a bunch of diodes in a ring to do the frequency mixing.

bitflipper
Ring modulators, which have been around since Moog Modular days, are used for inharmonic compound sounds, such as bell tones. Sometimes they're used for nasty electronic percussion. Beyond that, I don't know what they're good for.
 

Ring modulation results in inharmonic tones when the input frequencies are not harmonically related. If you feed the carrier and modulator inputs with harmonically related sine waves, you get harmonically related tones at the output. If you input more complex waveforms, you will get both harmonic and inharmonic output. Some ring mods only have a modulator input and use an internal carrier, in which case you will get  inharmonic output except for notes where the internal carrier is tuned to the audio.
 
If you want to play with ring mods, start with simple waveforms (sines, triangles, etc) for both the carrier and modulator, or use the same signal for both and ring mod the signal with itself. 
 
 
Bit reduction results in something between noise and weird, almost always inharmonic distortion. 

Thanks all for the replies, I know it wasn't a very specific question, inviting brainstorming. I see that the types aren't technically similar, but that with a FSU goal in mind either type might work. I guess I need to play around with ring modulators more - MRingModulator is just such a weird effect, it throws me. The only time I used it I mangled this spoken word part of a song in a way that was similar (to my ears) to what a bit crusher would do, but with slightly more control. Now that I listen to it again, I'm maybe hearing it through these more technical explanations of harmonic distortion...interesting how the brain and ears interact when you know a little more about the mechanics...
 
For reference, here's what I was talking about - the section starting at 2:05:
 
https://booleanoperators.bandcamp.com/track/self-portrait-with-horns
 
It's mixed low for texture and subconscious suggestion. The effect makes me sound like a certain disguised heroine rescuing her beau from an alien mob boss, I think. I'd been playing around with bit crushers for this part, but in the end the ring modulator fit the bill so much more.
 
Back to the lab I guess.