Yes, after the second pilot episode the science insignia and the ship services insignia were switched on the uniforms. That is why Scotty is wearing the science insignia in the second pilot episode and Astro-sciences physicist Sulu and Dr. Piper (and Dr. Dehner
) are wearing the ship services insignia in the second pilot episode.
I guess what I'm getting at is this: how do we know that the insignias mean "science" and "ship services" since they were used differently in the same series run? Example: Scotty goes from circular insignia in "WNMHGB" to reverse-C for many episodes and then sports the circular one again in "Lights of Zetar". And then the circular one again for more episodes. It doesn't sound like a mistake since the meaning of the insignia is not established and he had worn it previously.
Other ships (like the Constellation) don't appear to even have room on their insignia to differentiate between services (see Decker's insignia).
edit: Could the insignia be more of a ship or fleet identification rather than an indicator of service? Or something else entirely? The shirt colors already seem to suggest different services.