I think I saw it mentioned somewhere that helm had their own colors in some of the TOS movies. I could be wrong though...
The first movie, ST:TMP, continued the TOS scheme as directly as possible: Sulu was still at the helm, and still wore yellow, while Scotty was still down by the boilers, and still wore red. The movie just introduced a few nuances, so that the formerly red Security was now silver, the formerly blue Medical was now green, and there was a special color for "high command", that is, Kirk wore white rather than yellow.
This got a bit confused in the second movie where the plot called for a special "cadet color", and this was chosen to be red for some reason. That meant that Scotty had to wear a new color, and he got yellow. In the first movie, virtually nobody but Helm had worn that color, so some might have thought of it as "helm color", and later as "helm and engineering color". But it was never really intended to be that; it just happened that no other yellowshirts had prominent roles in the first two movies.
(In fact, nobody knows what would have been the correct color for engineering in ST2, since red had been stolen for trainees and nothing new had been introduced. Grey is as good a guess as any, systematically speaking, since that's what e.g. the formerly red Uhura wore, but I don't think we ever saw a grey engineer. Plus, the ship was on training duty, and probably full of instructors instead of regular officers, further confusing the colors.)
Helmsmen in the following movies continued to wear the TOS yellow - except in ST6, where both Valeris and her replacement wore grey instead (but Sulu's helmsman still wore yellow). In ST:GEN, yellow returned to Helm, as Demora Sulu wore this color.
On the deeper question of what the colors mean, in the movies they seemed to give a rough indication about the duties and specialization of the wearer. But this is not true in TOS or TNG, where there are dozens of specialities but only three colors. One might argue that the colors have a completely different symbology there. Say,
Red = unrestricted line officers (Yellow in TOS)
Yellow = restricted line officers (Red in TOS)
Blue = staff
That is, people in red (TOS yellow) are an upper caste, capable of assuming the broadest range of command duties. People in yellow (TOS red) have limitations on what they can command, as they dedicate more of their time to being good at their specialist jobs. And people in blue are pure specialists, subservient to the others.
This definition would jibe with the chat Sisko and Eddington have about the significance of yellow shirts (Eddington can't become a skipper while wearing that color), and with the fact that blueshirts in all the shows may hold high ranks but don't get to take command unless the circumstances are exceptionally dire, or otherwise exceptional. Spock is a major exception from that rule, tho. As are Captain Robau and Lieutenant Kirk on the
Kelvin, for that matter.
Timo Saloniemi