The nomenclature can be confusing as folks tend to use the terms "housing" and "bucket" interchangeably.
("I plead guilty, your honour, and throw myself on the mercies of the court. I have amended my ways and will sin no more. Well, I'll try anyway..")
In the M1102 manual at least, and to several manufacturers/retailers, the part that rivets to the trailers and Humvees that Springer shows above is referred to as the "tail light housing". The "bucket" usually refers to the cupped back that the incandescent light bits mount inside of, and which is empty for LED lights.
The lens holder is called a "door" for some reason!
Other than all the obvious internal bits inside the incandescent bucket, the difference between those and ones for the LEDs is that the LED buckets have flat mating surfaces, lacking the thin ridge the others have for engaging the o-ring in the door.
(That probably sounds confusing, I'll dig a couple out and take pictures).
You can put an LED onto a gutted incandescent bucket, it will just sit a fraction proud of the mating surface because of the o-ring ridge. Functionally insignificant, and it doesn't really show on recessed lights.
Cheers