The Next Generation’s warp core would become Voyager’s warp core. And before TNG, it had been the warp core going back all the way to The Motion Picture. The same set piece would be used and altered from 1979 through 2001 for multiple productions.
The Voyager core looks NOTHING like the TNG set piece. Exactly what parts are you saying they had in common?
So it turns out that the warp core originally made for Phase II (and first seen in The Motion Picture):
Was the same internal mechanisms – electronics, physical structure (wood and what not) throughout much of Star Trek.
The outer components and how the lighting worked was all that really changed between its uses in the various original films, The Next Generation, and finally Voyager.
Which is also why Voyager’s core looked different in the earlier years; it had a more TMP-era coloring before they made it a more solid blue.
So the basic underlying structure was the same set piece from Phase II set construction in 1977-ish all the way through the movies, through all of TNG, and until Voyager wrapped in 2001. It was just cosmetic changes on the outside that changed with each iteration. Much like so many other parts of Star Trek where continually recycled (corridors, bridges, consoles, props, et cetera).
I was surprised to know that myself, because you’re right: the Voyager core and TNG core look 100% different. But underneath they’re the same mechanics. I forget where I read the interview, but someone remarked how when they went to strike the Voyager sets it was like an archaeological dig with the warp core, going back from Voyager through TNG into the movies as they pealed it back.
I’m not sure if it was the same core used for the Defiant or Enterprise-E though. That I don’t know. The interview/article I read years ago only referenced Voyager, TNG and TMPs.