When making a gradient, when would you adjust the transparency options at the top of the gradient color rectangle? I can place stops to control how the colors transition, though I'm not sure how to use the transparncy stops work. Couldn't I drag on the control arm to do the same thing, control how the colors transition?
The control arm affects positioning, scaling, and rotation of the gradient, while the gradient editor allows you to fine-tune the gradient itself: adjusting the number of stops, their colors and positioning, alpha transparency, as well as direction and angle. (Direction and angle can also be adjusted using the control arm, so there's a certain amount of redundancy built-in, which is a good thing.)
You don't have to use all these features every time, but they're there when you need them.
The opacity stops allow you to introduce degrees of transparency into your gradient, which implies that you'll be layering the gradient on top of something else. For example, you could add a vignette effect to a photograph by drawing a rectangle and filling it with a black-to-transparent radial gradient. Then you can use the control arm to adjust its positioning and scaling, or fine-tune the transitions (smooth vs. abrupt) using the gradient editor, and so on.