In the original series, the iconic "delta shield" insignia worn on the uniforms of the crew of the USS Enterprise was seemingly not the entire insignia of Starfleet. In fact, in multiple TOS episodes, it's very clear that different ships have different insignias. But, in The Motion Picture, the famous symbol becomes the symbol for all of Starfleet.

Because this symbol is perhaps the most famous symbol in all of science fiction, it's significant that this movie is the first time it becomes representative of all of Starfleet, at least in terms of on-screen canon. However, since then, certain prequels (like Star Trek: Discovery) seem to make it clear that the famous symbol was used by other non-Enterprise ships well before the events of The Motion Picture.

So what's the deal? Some sources say that variant Starfleet insignia worn by the crews of other ships in TOS is simply a production error and that we should all ignore that stuff.

But, one thing is clear: This film is also the first time Starfleet uniforms changed significantly from their appearance in the original series. Obviously, after The Motion Picture, Starfleet uniforms would change a lot, but before this movie, the color-coded uniforms of "The Cage" and the original series were all fans had. And, in this film, it was strongly suggested that everybody could wear blue or beige or white and it wouldn't indicate anything about which division they worked in at all.

Also, this time around, it was hard to be a sacrificial "red shirt" since nobody wore red. (Even though by the next film, everybody would wear red.)