They're two totally different games, Super Air Zonk is as stated the sequel.
Here are some key differences.
Air Zonk runs much faster, this might be due to loading time limitations of Super Air Zonk being a Super CD, or lazy programming.
Super Air Zonk is super easy and allows you to pick from four different stages in the order of your choosing at the start (kind of like a Mega Man game).
In Air Zonk you'd transform by picking up a few of the giant smileys and picking a familiar/side character at the start of each level. In Super Air Zonk you transform by saving a familiar that is tied to that particular level at a point in the level. So you can't try different combinations in different levels.
Super Air Zonk has redbook CD audio, unfortunately I think the music is worse than the original Air Zonk.
Overall they're both good games. Super Air Zonk was a bit of a disappointment to me when I first played it, but having spent some time with it, I think it's a quality title. Just not as good as the original.
Also, last I knew both games were downloadable on Virtual Console (that's how I first played Super Air Zonk), so it can be played at a reasonable price if you have a Wii.