Perhaps Starfleet switched primary uniforms to the FC type, and at the same time decided that due to DS9's ever-growing importance that the senior staff should wear the formal uniform as opposed to the optional coveralls they all loved.
I always assumed it was intended to be a starship/starbase distinction in the TNG era. (Certainly this is what DS9: "Emissary" seems to be implying. Sisko, Dax, Bashir and O'Brien all wear the TNG outfit at various points in the episode, largely because they all arrive at the station directly from starship duty). Although the Real-Life explanation was far more mundane: simply a need to distinguish TNG and DS9 on a visual level, so that the new kid on the block looked distinct and unique from its parent for any audiences that were channel surfing. As for why VOY makes the switch, pre-production sketches for set designs etc for "VOY: Caretaker" show crewmembers wearing the standard TNG outfit, so I assume the decision to switch to the DS9 jumpsuits was made quite late in the day. Maybe even after the decision was made to use the DS9 jumpsuits in GENS when the originally planned new uniforms proved inadequate for their purpose. I do like the fan ret-con theory that the DS9 jumpsuits were ALWAYS an alternative uniform and it was just down to what the ship's XO considered appropriate for their mission.
Bashir's first assignment was DS9 - he didn't have starship duty before arrivin' at the station. He was obviously transported by the same Oberth-class ship that brought Jadzia, but that'd be about it. Also, Sisko's assignment before DS9 was the Utopia Planitia shipyards, which seems like a bunch of starship construction rigs & a station. Point is, not a starship. He, too, was ferried by one to the station.
As mentioned up thread it's probably supposed to be similar to how there is a uniform of the day in the military. Also, just like in the modern military they probably figured it was stupid to have multiple uniforms so they just streamlined it into the one gray uniform. The US Army for example went from having Dress Mess, Dress Blues, Dress Greens (combining both the class A and B variants), Dress Whites, BDUs and DCUs to simply the Dress Mess for super formal occasions, ASUs (modified dress blues) for business and the ACU for field work (though in practice ACUs are worn for everything).
We saw a lot of starbase personnel on TNG, always with the standard TNG uniform. Maybe I'm wrong, but until "Generations," I don't recall ever seeing any non-DS9 guest star in the DS9 uniform. It was clearly a distinction of some kind, you're right. Maybe it was the uniform not for all starbases, but for the Deep Space stations. While I wasn't crazy about the uniform change to the FC gray tops, it did allow for a really great WTF! moment, when we find out Bashir has been replaced by a Changeling and the real Bashir is still wearing the old uniform.
I was never crazy about all the uniform changes in the Star Trek shows. It got to remind me of comic books in recent years, where every new writer/artist team that comes along feels the need to give, say, Iron Man, new armor every few issues, after literally decades of the same one used. The worst costume decision to me was Yesterday's Enterprise, with the Enterprise C's crew wearing movie maroon jackets with no turtleneck underneath. It looked like one would dress in the middle of the night when an earthquake strikes: you just grab whatever is handy, throw it on and run outside.
From a production point of view, the DS9 uniforms were created to give the show a distinctive look different from TNG. I think the original intention was that the DS9 uniforms were meant as a utility uniform, something officers would wear in a more 'gritty' environment. The reason VOY inherited the DS9 style uniform instead of the TNG was a cost saving measure. The TNG uniforms were getting worn out, so rather then creating new ones, they could 'split' the uniform costs between both shows. When DS9 switched to the First Contact style uniforms, VOY inherited all the DS9 uniforms. I also believe that the costs to make the new style uniforms for the DS9 cast, was absorbed into the FC budget rather than DS9's budget. One piece of Trivia: Star Trek Generations was supposed to debut a new Starfleet Uniform but apparently they looked bad on screen so they switched back to the TV uniform. However, Jonathan Frakes DS9 uniform was actually Avery Brook's and Levar Burton's was Colm Meaney's. Only Patrick Stewart and Brent Spiner got custom designed DS9 uniforms.
Yeah, that was the cadet uniform. The first time I saw a publicity shot of the DS9 cast I kept wondering why they were wearing cadet uniforms.
The idea was originally conceived as starship crews wore the TNG uniform and starbase crews wore the DS9 one. Of course, after DS9 started we never saw any starbase personnel on TNG, although whenever we saw starship personnel in DS9's first few seasons they did wear the TNG uniforms. As I understand it, the original plan with the new uniforms that were designed for Generations was that they would continue the ship/base divide and those uniforms would then be used on Voyager. But of course, those were ditched at the last minute and due to a desire to make Generations look different than TNG, they wore the DS9 uniforms. But then, budget constraints meant they literally had to wear the same costumes used on DS9 and there weren't some to fit some of the actors, resulting in the weird mix we saw in the movie. Voyager likely went with the DS9 uniforms because someone high up felt its cast looked better wearing those than the TNG uniforms.
Changeling Bashir has an interesting line to Sisko in the first appearance of the grey uniforms: In the context of the episode it makes sense (Sisko's vision has been affected) but I found it weird because the new uniforms were more monochrome than anything before!
Do personnel on docked ships wear Docker's? Humans have told me that black is a slimming color, so I wear black jumpsuits during my off-duty times!