I ended up typing an entire wordy essay, during which you figured it out. The compressor sounds smoother because it works over a larger range of the music's dynamics. A limiter cuts in harder and just effects the loudest peaks. But they are really two cousins. Like mallet and a ball-peen hammer.. so on to the essay:
I find that drawing in a volume envelope like Brian suggests is easier for me to get sounding right, if more time consuming to do. The volume envelope is easy to understand and supremely suited for adjusting long duration events like louder applause or cheering between songs. It's still straight forward, but harder to get just right for screams, claps, or short sounds in the middle of a song. Importantly, the volume envelope doesn't change the dynamic range of the music all the time like a limiter or compressor. It only changes things when you move the curve up or down, by moving the entire dynamic range up and down and making everything louder or quieter. As long as the volume envelope is flat, the micro dynamics moment to moment in the music are unaffected, so it won't effect the sound at all between volume changes.
The two controls you mention are maybe a wet/dry mix control, and release ?
Attack and release controls effect how fast a compressor/limiter engages itself on loud events and how fast it reverts to not doing much. The analogy to the volume envelope is how steep you draw in the envelope change, except usually a compressor is making many more changes than you would be drawing in. The sonic effect can be subtle (or not) and tricky to set right. It effects how well the compression/limiting effect blends into the music and often effects the tone as well. Getting that setting right can be the difference between hearing the compressor squashing the music and not noticing it doing it's work, for the same overall reduction of range.
I think the wet/dry mix is one of the coolest tools in a compressor for what we need. A typical compressor is all dry- you only get the effected (squashed) sound out the other side. A 100% dry setting would be no effect at all, same as the input. So why would that control be useful? Because with a 100% wet output the result is the compressor only doing it's work on the 'loud' parts. What it considers 'loud' is controlled by the threshold setting. The wet/dry control is a way to do what's called parallel compression - effectively mixing the compressor's output with the non-compressed signal. Doing that lets the loud parts though again unsquashed. But if the threshold of the compressor is set so it is working more or less all the time, then the quiet parts are brought up in level by the squashing effect of the compressor making them louder. Parallel compression effectively makes a compressor a bottom up tool instead of a top down tool. That can sound more natural, possibly because it is doing less work on the major portion of the music.