At the end of Revenge of the Sith we see this as one of the final scenes:
We clearly see that the first Death Star has most of the super laser dish constructed and a lot of the reactor core and super structure is in place.
However, in Rogue One, we see this:
This is the Death Star that we've come to know and love in A New Hope, so what is with the discrepancies between them? Was the one in Revenge of the Sith just a prototype, was the dish a placeholder and the real one was put back in?
The Rogue One Visual Guide is quite clear that the dish we see being installed is the one that was functional:
Superlaser
After a long wait, a stable, operational superlaser assembly is guided into the Death Star superstructure and connected to the hypermatter reactor.
There are multiple confirmations that they're the same station, rather than one being a prorotype:
Hidalgo has said multiple times on Twitter that the Death Star itself took twenty years to get functional, not to build; for example:
@pablohidalgo There's one specific part that took years to perfect. It's not like it took 19 years to build the whole thing.
The Databank confirms:
Even as the Clone Wars raged, the Death Star secretly took shape in space above Geonosis. Access to the former Separatist world was restricted, with very few in the Imperial hierarchy allowed to know about the battle station’s construction.
It's quite strongly implied in the Rogue One Visual Guide:
A Death Star Begins
Using captured Geonosian plans procured by Palpatine, construction of the Death Star is secretly started over Geonosis, under the supervision of Tarkin and Krennic.
Construction Over Geonosis
Enormous orbital construction domes begin transforming the rocky rings of Geonosis into raw construction materials. A spherical shape beings to emerge.
Kyber Transformation
The lack of a functional superlaser slows down the Death Star operation. It is not until Galen Erso is coerced to research kyber dynamics that progress is made.
Final Fitting
The final functional superlaser - created on Eadu - is transported to the Death Star where it is fitted into the superstructure. The Death Star is finally operational.
The canon novel Catalyst (the prequel novel to Rogue One) depicts a continuous construction process from 21 to 17 years before A New Hope (or from 2 years before to 2 years after Revenge of the Sith), and the novel Tarkin indicates that the construction was still ongoing by 14 years before the film (five years after Revenge of the Sith). It's hard to provide evidence for this without citing most of Catalyst, so you're going to have to trust me.
Whether the original dish was a placeholder or not is unclear, but Hidalgo's implication is absolutely clear: the dish we see at the end of Revenge of the Sith is non-functional (or, at least, non-properly-functional), but the one in Rogue One actually works.
I don't think the dish is being "installed" as much as repositioned or configured. It could just be in the middle of positioning for maintenance, calibration or aiming. Moreover, I would imagine that being able to remove or at least create a space to work behind it would be important to its development.
But here's a little more context around the dish's use and capabilities from Catalyst:
The plan, in any case, called for assembling the dish in space and maneuvering it by tug and tractor beam into the gargantuan well that had been framed into the sphere’s upper hemisphere—the dimple, as some referred to it. The parabolic dish also had to be engineered to telescope away from the hull to facilitate the aiming of the composite beam proton superlaser some of the Special Weapons scientists were proposing.
So really, the fact that the dish was "popped out" at the time of the scene might have nothing to do with it being "under construction" at all. And I think the image from Revenge is the "gargantuan well" that this is referring to.
I don't think the concave portion of the Death Star shown a the end of ROTS is a dish at all - rather, it is merely the framework which is ultimately going to support the actual dish when it is installed. [That's why it has holes in it.]
