I am looking for a single word that describes this thing (1):
but not this thing (2):
The obvious choice here would be pentagram, but in colloquial use, that word unfortunately refers to both (1) and (2), as well as a number of variants of (2) that have other enclosures surrounding the 5-pointed star. (In mathematical use, "pentagram" uniquely refers to (1) and not (2), but I am not writing for a mathematical audience, so that's still a no-go.) It also has connotations I would like to avoid (devil worship, goat sacrifice, etc.).
If all else fails, I can just call (1) a "five-pointed star", but that gets to be a bit of a mouthful.