That's a pretty good analogy. Technically, compression is measured in a ratio, such as 2:1, where 1 db comes out for every 2db the signal goes over the threshold. For low ratios, you have compression, such as the above, where 10db over the threshold would still give you 5 db out. Higher ratio compressors become limiters. Usually over 10:1 is considered the beginning of limiting. There is brick wall limiting, which is essentially infinity:1.
The speed of the attack and/or release is also a consideration, where compression can have quite slow attack and or release (and in fact, slow release is pretty much a necessity for bass compression because if it's too fast, it interprets the actual wave as individual notes and can result in distortion) whereas limiting tends to be very fast attack and release. Having a slow attack can allow the articulation of the note through at the beginning, but then bring down the level. This can accentuate the attack of the note. Having a fast attack can clamp down on the initial impulse of the note (often the loudest part when measured) and then with makeup gain, the sustain can then be made louder, giving the sense of a smoother tone. So, compressors are very powerful and can create quite a range of sounds.
Noise is not a necessary artifact of compression. My Grace M103 (preamp of choice these days) has a compressor that is capable of quite a bit of compression and adds no noise whatsoever. Where compressors gain (pun intended) the reputation for being noisy is that after you've compressed the signal, often you add gain on the output which brings up the noise that was in the signal before the compression. Limiters can also create this consequence.
So, at the end of the day, they are related. Both are useful for bass, depending on your sonic goals.
(Message edited by edwin on February 18, 2013)