Yeah, the lowback Security Six could be had with either fixed or adjustable sights. This is from the 1970 dealer price sheet:
When the frame changed to the highback, the fixed sight version was renamed to Police Service Six. And yes, there were a few contract guns marked simply Service Six.
To my knowledge, there were no lowback fixed sight guns marked Police Service Six.
The confusion at the factory (where it is a whole new generation of folks with no memory of the 1970's) is due to both named models sharing the SDA catalog number prefix (a .38 with a 4" barrel being SDA-84, and the 2.75" barrel being SDA-82). And in spite of being listed, I don't think there were any 6" barreled fixed sight guns produced in either frame.
I have collected a good sampling of guns on either side of the 150/151 transition and have highback 150 prefix guns marked Police Service Six in both .38 and .357. I have lowbacks in the 151 range but I don't believe I have any fixed sight 151 lowbacks.
The white boxes with the die cut interiors would not properly fit the highback frame contour, so the early highbacks were shipped in the flimsy red/white boxes used prior to the heavier red/black boxes.