You generally want to dither when (before) you quantize, unless you have so much headroom that it doesn't matter. E.g., if you're converting 44.1/16 to 48/16 (which involves quantizing each sample from an intermediate higher-precision result), you probably want to dither, but if you're converting 44.1/24 to 48/24, you probably won't need to care since you don't really care about whether your effective result is 24 or 24.5–25 bits.
That's more of a bit depth rather than bit rate thing. I was surprised to find that going from 16 to 8 bits by simply truncating gave really obvious artifacts on certain sounds (a sampled 808 kick for example had a distinct BZZZEEEOOOOWWWW sound, quite prominent), and even really simple triangular noise dithering made it go away. It did mean the playback was more noisy but it was less obvious.
As an aside, G.711 codecs use a kind of log scale with only four bits of signal but small signal values use much smaller bits.
The word dither -- evidently, the term dithering originally referred to a trembling or erratic movement, from the Middle English didderen, meaning "to tremble."
further, the halftone technique developed in the 1880s by Georg Meisenbach — breaking images into dots to simulate shades of gray — was called autotype, not dithering. The term dithering was later adopted in digital imaging and computing, particularly in the 1960s, when engineers applied the concept of adding noise to reduce color banding.