This is my little family of Singer zig zag attachments and here are samples of the stitching (begging pardon for my sloppy, crooked rows).
Stitch quality is almost the same - in fact the two earlier models actually make a slightly better satin stitch. But all make a perfectly nice zig zag. Here is the difference in operation. The oldest model works like this (bight is adjust by a screw in the back):
This one runs a tad smoother, I think, but the main advantage is that you can change bights to N-M-W with a gauge on the side rather than just a screw on the back like the older model.
These two models both come with an edge stitcher which can be attached so that you can stitch on the very edge of the fabric or join a piece of lace right to the edge like this:
And they also have a cording slot so you can zigzag over a cord or thread for gathering. Very useful!
The most contemporary model is also the biggest. It is actually rather huge! This is the Singer Automatic Zig Zag Attachment which takes cams to make different decorative stitches. Here it is in operation doing the zig zag stitch and a deco stitch:
This is a rather amusing gadget which makes surprisingly nice stitching. It comes with a set of four cams, and three more sets of four are available. I have all except the BLUE set. (still looking!) But the drawback, apart from the clunky size, is that it does not have the edging attachment. That makes it very difficult to do some of the tasks that you would normally do with a zigzag such as stitching very close to fabric edges to finish seams, doing lace insertions, or zigzagging over cording. I look at this model primarily as a decorative stitcher.
The first model - the oldest one - not only works great, but is small enough to pop into my Featherweight case. Actually it isn't any bigger than the standard issue ruffler attachment, and somehow it's dainty size just seems more suited to the FW.
So why do I even keep all these around when I have a Slant-o-Matic to do my zigzagging? If you have to ask, then you just haven't played with vintage sewing machine attachments enough to know how fun it is to use them! :)