In the following image we have squared, rounded, lined and dashed objects. Each object is labeled with its name, but I have a situation between squared and rounded objects. What name would you use for this object?
Rounded corner or just Round Corner. Adding the "corner", to me, means there's an apparent corner as opposed to the Pill shape.
As @Wolff points out in the comment above, both the pill shape and the shape preceding it are "rounded" shapes, merely the radius of the rounding varies. So.. I'd use a more specific name for what you've labeled as "rounded".
I'd probably change the list.
I quite like "cartouche", as a single word. This is a good alternative to "stadium" or "pill" etc for the middle symbol, but I don't have the reputation to comment that!
There is a certain class of shapes unifying the ellipse & the square, but its name isn't a common term or applicable to other generalizations. Piet Hein, who invented the Soma cube, also gave the name superellipse to a class of curves generalizing the ellipse which in the limit includes the square. It was described in Martin Gardner's Scientific American Mathematical Games column (written for the general reader). (The superellipse & its 3-D solid of revolution, the superegg, turn out to be deceivingly metastable; they tilt but return to upright when not pushed too far.)
I have always known that shape as a 'Roundrect'.
Another suggestion, in the style of Scott's answer, for these fairly long rectangular buttons (bold text is my new suggestions).:
Squared - rounded* - round-ended - outline - dashed
* (or round-cornered)