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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."

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The visual impression would suggest something like "inflated" - Fig.B's points have moved (approximately) like they would if the star was attached to a sphere. –  Pekka 웃 Apr 23 '11 at 7:31
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How about a filled pentagram for the first, and... um... er... uh... the other thing for the second? (^_^) –  RegDwigнt Apr 23 '11 at 11:20
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Note that figure B technically isn't a pentagram, because it can't be drawn in five straight lines. The word comes from Greek (here I go again): penta = "five"; grammê = "mark, line" (from graphô, "to write or draw"). In fact figure B cannot easily be defined, because I imagine the angle of its tips is variable, as this angle is not a function of any other line or angle of the figure. –  Cerberus Apr 23 '11 at 13:38
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@Cerberus: exactly my point. The second figure is not a pentagram. That's precisely why you can distinguish figure A from figure B by saying that the first one is a filled pentagram but the second one is not. They are both filled. But only the first one is a pentagram. Am I repeating myself yet? (^_^) –  RegDwigнt Apr 24 '11 at 19:24
    
@RegDwight: I see. So what is your point? You are still asserting B is a pentagram? // Okay, okay, I'll stop joking! I don't quite remember why I posted that: it seems almost as though I hadn't seen your comment. Reading back, I don't understand why I didn't write "as Reg says, ...". –  Cerberus Apr 25 '11 at 0:19
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2 Answers

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.

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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).

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