Stretch fabric is knitted, rather than woven. You can get some woven fabrics with elastic fibres, like stretch denim or stretch poplin - these have minimal stretch and can be treated like a standard woven. For now I'm focusing on t-shirt fabric, ponti and really stretchy lycra/spandex stuff.
Because of the difference in construction, you usually need a ball point, rather than a universal needle. This allows the needle to push between the gaps in the knit, rather than piercing it. In a woven fabric, you want to pierce a hole so you don't snag a thread and create a pull in your work. In a knit, if you break the strand, you get holes. Ballpoint needles may be sold as ballpoint, jersey or stretch needles. To the best of my knowledge, jersey and ball point are the same, but stretch needles have a slightly different shape/eye which makes them more suitable for super stretchy stuff like lycra. Get those if you're doing swimwear.
|Pointy for woven fabric, rounded for stretch fabric.|
Sometimes you can get away with a universal needle on stretch fabric. Its easy to test. Before you sew your garment, grab a scrap of your fabric and do a test run. Pull it out and hold it up to the light. If you're seeing any holes forming around the seam / stitches, you need a ball point needle. Change it now, save yourself the disappointment. These little holes have the potential to run - just like a snag in a pair of stockings or a knitted sweater.
|It's not going to get better.|
If you are wondering about coverstitch, just to go on a tangent here, it is this stitch:
Which you will have no doubt encountered on the bottom of every t-shirt/pair of leggings you own.
Sadly, that's not a stitch you can do on a regular domestic machine. For that, you require a specialised coverstitch machine, or an overlocker with a coverstitch function. It's a bit fussy to work with (because if you sew without fabric in there, even one itty bitty stitch on the handwheel, the whole thing jams up) BUT I think worth the trouble. Unfortunately, my overlocker/coverstitch machine is sitting in storage on the other side of the planet. Bummer.