Not the same anon, but why did you use elastic thread in your last fully shirred jsk instead of a non-stretch polyester/cotton thread for the shirring? I've always (read: 4 times) used the same thread as for the rest and just let the elastic bands do their job. Is this just about preference or does it actually work/look/feel better?
Short answer is that there was no elastic bands other than the elastic thread in the bobbin. It's just a different technique of shirring.
There's sort of three ways that are common to do shirring: elastic channel, elastic topstitching*, and elastic in the bobbin.
Elastic channel is where the face fabric and the lining are sewn together into channels. The elastic is then fed through the channels and secured at both ends. This allows you to have a lot of control over what size the finished piece is, and let you change that elastic length without changing the garment. It ensures that the fabric is going to self-distribute evenly across the different lines, because it allows the fabric to move around the elastic, instead of being tethered to a specific piece of elastic. Elastic channels have two lines of stitching visible from the face of the fabric.
Elastic topstitching is where the elastic is sewn directly onto the garment, being stretched as it's sewn. This way is a lot faster than elastic channels, and it doesn't require a lining. Because you cut the elastic before you sew it on, you have control about what the length of the shirred piece will be. Because the fabric is directly tethered to the elastic, you cannot shift the fabric around once the piece is shirred. If something is off-center, it's off-center forever. You also can't shrink a piece of fabric that is longer than the max distance the elastic can stretch. Elastic topstitching will leave a single line of stitching on the face of the garment.
(Image shows three lines of elastic bobbin applied next to each other)
Elastic bobbin is when you wind your bobbin in your sewing machine with elastic thread, which will apply the elastic to the garment whiel you sew from the top side. Elastic bobbin thread gives you the least amount of gather, and the least amount of control about how much the fabric is gathered. The elastic thread is much weaker than any elastic you'd directly stitch on or put into a channel, so it won't pull the piece in very much. However, elastic in the bobbin also requires you to do no measuring, and it will (or should) distribute the elastic evenly across the dress with very little effort.
If you're doing a fully shirred JSK, doing elastic channels is generally the best bet. Because a lot of us who wear lolita have boobs, and therefore more than half of our chest measurement comes from the front of our bodies, we often need to shift the fabric around so that the distribution isn't actually completely even.
If you're doing a half- or full-back shirring panel, you probably want the strength of actual elastic. Elastic bobbin doesn't gather very much, and it might not be strong enough to hold a dress in place. In addition, smaller shirring panels aren't as difficult to add elastic to as fully shirred pieces are, so you don't save very much effort by doing elastic bobbin.
Elastic bobbin requires multiple parallel lines of gathering to actually do any real shirring. You can't use it in most places where you would normally add elastic. It's main advantage is for multiple lines of shirring. It is a very handy technique to use on the ends of sleeves to make them puff, and you can do several rows about 1/4" apart at a neckline to gather it up. I did that in the this tutorial.
Elastic bobbin will always require some experimentation on your machine to figure out how it will work. It almost never works on the first try.
I learned the elastic in the bobbin technique from this video, from back when Threadbanger did sewing tutorials. However, I wind the elastic thread onto my bobbin with the bobbin winder, ensuring that it's all the way stretched when it goes onto the bobbin. This gets the most gather possible, and makes sure that it's fed evenly onto the entire bobbin. You just can't store the bobbin in this way, or else the elastic will die, so unwind it and throw the remaining thread away when you're done.
tl;dr
Elastic channels: Most control, allows the most gather, will self-level to ensure evenness, can be a pain in the butt, requires a lining, best for full shirring
Elastic topstitching: Fast, allows control of the amount of gather, possibility for lumpiness if you're not careful. Fast way to make shirred back panels, doesn't require a lining.
Elastic thread: very little control over amount of gather, very easy way to apply a lot of elastic very quickly, weak gathering power and cannot be load-bearing, not as many applications.
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*not technically topstitching, but the stitching is seen on the top, and I don't know what else to call it.