I imagine that the coding rate establishes the number of times (per second) that a new sample is taken, with incremental changes being used to rebuild the recording between samples. Is this so?

It sounds like you're confusing sample rate with bit rate.

All MP3s usually have the same sample rate: 44.1khz (the sample rate of the CD they were ripped from).

The bit rate (128, 160, 192, etc.) controls how much data compression they apply to the music. A lower bit rate means that the sound is data compressed more heavily, resulting in more compression artifacts. However, the sample rate (44.1khz, or 44.1 thousand samples per second) doesn't change.

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Tony Fabris