We saw the Reliant studio model four times during TNG/DS9/TNG films.
1. Lantree, a Class 6 supply ship with a crew of 26.
2. Brattain, a science vessel with a crew of 35. (First use of the name 'Miranda class' on the dedication plaque)
3. Saratoga, a standard active-duty starship, crew number unknown.
4. Saratoga, a standard active-duty starship rescuing survivors from Veridian III (same name and registry number as above ship despite above ship being destroyed earlier, since the info was never removed from its previous use.)
I am of the opinion that both the Lantree and the Brattain were originally supposed to have been much smaller TNG-era ships distinct from each other, and not reuses of the Reliant filming model from the TMP films. But the producers didn't want to build new models. I also believe that the only reason why the Reliant model was used for Sisko's Saratoga was because it was the smallest in-universe Starfleet vessel (minus the Oberth class which was not a warship) that they could film up close because the model had sufficient detail. I think that if DS9 had a bigger budget, the Saratoga would have been a new model and a new class.