Welcome to the forum!
Those buttons on the control bar are not for making an arc or wedge, but for choosing arc or wedge, after you already "open" the ellipse or circle. To do that, grab the tiny circle handle on the right of the ellipse/circle, and drag. Or the other way would be to put a non-zero value in either Start or End fields. In any case, once it's "open", you can click either one of those buttons, depending what you want.
Note that I use the word "wedge" to describe what this button makes
and "arc" for this button
. Normally I try to stick to Inkscape terminology. But Inkscape calls what I call a wedge, a "segment", which I find confusing in a few different ways.
Another interesting thing to note, is that you don't necessarily have to click either arc or wedge button. As you drag the tiny circle handle, if your mouse is inside the original ellipse/circle, Inkscape makes arcs. If your mouse is outside the original object, it makes wedges.
Interesting, a rainbow was the very first thing I tried drawing with Inkscape, too! But I had not yet discovered the fact the Ellipse/Circle tool could be used for that. I was trying to use the Pencil tool!
