Actually, the five-point star enclosed in a circle, as you describe, is called a pentacle. The pentagram is the star it self. The pentagram has five points with each line drawn straight through, allowing intersecting lines to be made. Thus drawn in five strokes. Commonly with neo-paganism, the pentagram/pentacle is seen as being associated with, earth, air, fire, water, and spirit. As well as with magick, protection, the universe, and other associations. However, other belief systems have been known to associate the points with different element sets. A pre-modern association was very similar to the microscopic human concept in that the early Christians used the pentagram to symbolize the 5 wounds of Christ. In short, what the pentagram associates with, if any in particular, is up to the individual.
Concerning elements there's a method of invoking elements based upon how the pentagram/pentacle is drawn; starting point, direction, ending point. Same goes for specific ways in which one banishes/closes/departs (what ever you wish to call it) the elements invoked in said manner.
Sure, the inverted pentagram/pentacle has been associated with satanism for being able to draw the baphomet goat head within the star, but truly it's no more evil than the pentagram. It's an opinion that rests in the eyes of the beholder.
You could even take the hexagram (six-pointed star) and make various associations. The Star of David. The sword and chalice united. And even here the baphomet again, but one with a an additive of a lit flame atop the head for the upper point.
All in all, the matter is not so much what the pentagram means, but rather a question of "what does it mean to me, if any meaning there may be?" that the individual may ask his/her self.