I'm surely no expert, since I avoid these things like the plague. I just did a bit of cruising around the web searching for 'limiter versus compressor'.
I believe you are correct, and your 'seems that way' comment nails it. A compressor is different than a limiter, which is the point that some are making above, if I have this correct. A true compressor can be set to greatly reduce the initial attack, and then this reduction level is 'reduced' as the note fades, increasing sustain and making a softer note 'seem' louder. Then, the 'make-up gain' amplifier is used to put the entire signal back up to the original line level volume.
Here's a representative blurb:
Besides serving as an automatic volume control, a compressor can also make notes sustain longer. To increase a note's sustain requires raising the volume of a note as it fades out. That is, making the trailing part of a note louder to counter its natural fadeout is what makes it seem to sustain more. To do this with a compressor you'll set the threshold low enough that the volume is reduced most of the time. Then as the note fades the compressor reduces the volume less, which is the same thing as raising the volume. For example, when you play a note on an electric bass the compressor immediately reduces the volume by, say, 10 dB because the start of the note exceeds the threshold by 10 dB. You don't hear the volume be reduced because it happens so quickly. But as the note fades over time, the compressor raises the volume which gives the effect of adding sustain.