Entirely different?
It's of the same class is it not? Though wouldn't be perfect I guess as each ship was modified differently over time by their engineers but I doubt that would be an issue for Geordi.
Yup.
I'd have imagined that they were fully standardised at least in the hull and connectors, especially if for example they were ships built in close succession.
Even if they were built a decade apart in most real world (and i'd imagine ST) fleets they'd try and maintain them all to similar standards via planned refits*, and IIRC star fleet has shown they'll keep ships in operation for 50-100 years, which indicates they'd certainly be built with future usage in mind.
Not to mention there has been at least one or two canon ST ships that had things like the entire warp drive pylons replaced either due to damage or to improve performance/for experiments, which is likely much harder than fitting a fully working engineering section to a largely intact/repaired saucer section.
I think there was also at least one episode where it was commented on that another ship of the same class as the Enterprise D had a newer/upgraded engine and that the D was due some time in dock to perform the same upgrade, and the modifications that were IIRC meant to be rolled out to all ships after the Warp speed rips space story.
Also as it was stated that Geordie had been working on it for 20 years, which suggests he would have had plenty of time to work out and solve any major incompatibility issues, and probably 35 years or so of Star Fleet maintenance records and what appears to be a major engineering facility to assist**.
In short, think of the Enterprise D as being an overgrown flying Semi in regards to docking the "tractor" with the "trailer".
*It's quite common for ships to be 40-50 years old in some major navies, but having equipment fitted that might only be 5 years old and wasn't dreamed of at the time the ship originally went into service.
**It's a "museum", but it's also a fully functional space station that is designed to show off and maintain ships, complete with at least one major internal work bay, given the damage a ship alone can repair I'd imagine the station is far better equipped as standard and probably able to rebuild/build from scratch major components (especially remembering what DS9, an outdated barely functional station was able to do even before the federation started seriously upgrading it).