The history of different costumes in Trek (real story, not in story exscuses):
The original TOS uniforms were really cheap and corny (even for the time period) so when they made 'The Motion Picture' they decided to create new and better uniforms. Of course, Gene Roddenberry was very much hands-on on all design for the movie and because he was a senile hippie, the uniforms he designed were pretty much just pajamas. The fans didn't like it.
Now, Paramount realized that maybe giving Roddenberry so much power over the franchise wasn't really such a grand idea. Fans were asking for more 'space adventure' and less 'new age mythology', so for 'Wrath of Khan' his involvment was really cut down. Director Nicholas Meyer hated the TMP uniforms and wanted more gritty, army-lookin' uniforms. Those uniforms remained with the film franchise until 'First Contact'.
Then there came TNG, where Roddenberry finally got some power over the franchise again. Not going quite as radically into the pajama direction this time, we get the season 1-2 TNG uniforms. They were cheap and badly done and very uncomfortable.
When TNG got renewed for a third season, got a budget boost and Roddenberry had to leave the franchise because of health problems, the uniforms were all redone. It followed the same basic design as the 1-2 season ones,with some minor changes, like the collars, but were much more expensive and comfortable. Some cast members then got new uniforms in the fifth or sixth seasons that are slightly different, because the old uniforms had been worn out.
New cheaper, more durable yet comfortable uniforms were made for DS9. TNG was not made change over because it was too expensive to make new uniforms for a show that only had one season left of it's run. In 'Generations' stock costumes from DS9 were used on extras because the movie got it's budget cut considerably early in production. When Voyager started they used the DS9 costumes as well, which are made out of a slightly different material, but otherwise completely the same.
'First Contact' got a huge budget, the largest for a Trek movie up to that point. To go with the darker nature of the movie, the producers made the grey costumes. When the filming of the movie was over, DS9 got the First Contact uniforms (the exact same ones). This was not the original plan, DS9's producers just asked for them, thinking that the tone of the costumes would fit the upcoming war arc of the series. As the series progressed you can notice that some of the costumes used on the extras in seasons 6-7 are slightly different than the ones used by the main cast. These are new costumes manufactored with DS9's limited budget.
Voyager never changed to these costumes except for the people they contacted in the Alpha Quadrant (that borrowed DS9's costumes), because Braga preferred the old ones and they got a pretty good exscuse not to switch.