When I was a young'n watching the show for the first time in the early 70's back in the glory days of UHF, I always figured the reason that Decker and Tracey had different patches was to show that these other officers were obviously NOT from the Enterprise. This made perfect sense. And they both looked kinda neat, better than the Enterprise patch even.
Conversely, until years later when I read an interview with Win De Lugo, I never understood why Enterprise crewmembers--junior officers no less--in the Starbase 11 bar were harassing their own captain over Ben Finney's death. And why did Kirk claim he hadn't seen them for a long time? What a bad commanding officer, not interacting with all his crew on a regular basis! Were they stuck working in remote areas of the ship for years and only now got shore leave so they actually could talk to (or more accurately, harass) their captain???
It's amazing how that all confused an eleven year-old watching "Court Martial" for the first time.