We tend to use the terms "tension swatch" and "gauge swatch" interchangeably.
For me, the gauge swatch is the "official" swatch when designing a garment. It is knit at a specific size, marked for accurate stitch and row measurement and "dressed" as the final garment will be treated. There are a number of tutorials in the Knit it Now Learning Library on this subject - Accurate Gauge Measurement
When I pick up a new cone of yarn, I can't wait to thread up my machine and see what the yarn looks like. From the initial cast on, I start guessing what setting on my tension dial I need to use. I knit a few inches and reach down and start to feel the resulting fabric.
Once I get a feel for the yarn (what machine, general tension setting at stockinette, etc) I create a tension swatch. This helps me fine-tune the tension needed to achieve the fabric I like and allows me to play with various techniques. I'm often very surprised that a yarn looks great in tuck, and awful in slip, for example. Adding a few eyelets here and there tells me if the yarn will work up in lace.
Depending on time (and patience level) here's an idea of how I knit a tension swatch.
The point of this exercise is to put the yarn through it's paces ... ignite your creativity, and get a feel for what the yarn can do. If you don't have a huge cone, you can always re-wind this knitting.
At this point, you probably know exactly what you want to do with this yarn. Knit your Gauge Swatch, dress it and you are ready to design and knit your garment.
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