If you want to get technical (accurate) about it, the top star is composed of rhomboids (adjacent sides are unequal lengths) and the bottom one is composed of rhombuses (all sides are equal length). It's like the difference between a rectangle and a square, but with non-right angles.
https://en.wikipedia.org/wiki/Rhomboid
I learned the top one as Eight Pointed Star and the bottom one as LeMoyne Star (aka Lemon Star). The proportions are different between the two no matter how they are constructed (inset seams, HST's, etc). The top one is a 4-patch block and the bottom one is a 9-patch block.