What are the proper terms for these star shapes?

Question

Both figures are star pentagrams. But as you can see, the shapes are different due to the degree in the angles. Are there proper terms for these two shapes? I find myself having a hard time describing the different type of stars to my designer friends. I'd say something like "I meant the straight edged ones, not the relaxed ones."

Answer 1

The proper term (i.e. the geometric term) is simply star polygon.

Of course this does not really help you in differentiating between them.

Inkscape speaks of spoke ratio defined as base radius to tip radius ratio, in the parameters where you can determine the shape of the star. I think this is a good way to distinguish them as you can actually put a number on them. So, for instance, the left star has a lower spoke ratio than the right one.

Both the stars in your example are straight edged, which I would understand more as opposite of something with curve edges.

Answer 2

I've heard this called a "fat star" or a "gold-seal star":

The other option in the dropdown is “Star”, and as you would expect it draws star shapes that also depend on the Number Of Sides you specify. Star Point Size is the ratio of the inner point of the star relative to the outer point. A value of “0.5”, for instance, will produce a “normal” star with balanced star points, with the inner point at 50% from the center, relative to the outer point’s 100%. A lower value will start to produce more “burst”-style shapes, while a larger value approaching 1.0 (which is the maximum) will produce a “fat” star or a more “gold seal”-style shape.

From this link (PDF).