While the exact look of the Starfleet insignia has changed with just about each new entry into the "Star Trek" canon, it has just about always retained its core arrowhead shape. However, even dating back as far as the original series from the 1960s, the symbol contained within each variation of the arrowhead has actually been used to denote the specific division of Starfleet that the corresponding individual is a part of.
Of course, the most popular variation and the one most commonly seen today is the logo with the star inside. This version is commonly used to denote a Starfleet employee who is a member of the command division. Most of the major characters who make up the crew of various starships, from Spock to Captain Picard, are part of the command division, hence why it's the most common variation.
"Star Trek: The Original Series" further introduces three other major variations. The one with two overlapping circles signifies a member of Starfleet's sciences division, the one with a spiral inside represents the operations division, and, finally, the one with a red cross contained inside belongs to medical personnel. Other "Star Trek" projects have introduced the occasional new variant, but these four comprise the most well-known versions in canon.
