To expand a little:
All three games (at least the versions I've played - Sega Genesis port of SC1, Ur-Quan Masters open-source project on PC of SC2, and original PC-DOS release of SC3) have some sort of meta-strategic mode to compliment the tactical.
In SC1, it was a very basic map of stars that you could slowly spread bases over while fighting it out in Melee combat all over the place. There was some VERY loose story about the ongoing war against the Ur-Quan, but most of that played out more in the manual than the game itself.
In SC2, the story picked up after the loss to the Ur-Quan, and was a little bit like an adventure game in space. As you explored star systems with your (growing) fleet, you'd get to engage in diplomacy with aliens and hunt down mysteries. To keep yourself flying, you also had to engage in a planetary lander mini-game, where riskier, harder-to-navigate planets usually bore out larger resource rewards to let you build and maintain a fleet comprised of ships from the alien races you'd convinced to join your crusade. Conflicts were handled in Melee, as above.
SC3 was taken over by another developer at the publisher's behest, and their background was strongly in adventure games, so that side of the game became much more focused and obvious; I recall more than a little fiddly item-combining to slot into just the right quests to progress the story, which featured a daring journey to the center of the galaxy where a whole new cast of villains and allies awaited alongside most of the old standby's. The planetary lander minigame was replaced by a somewhat involved 4X-style map-conquest mode, like a more-advanced version of what SC1 featured, where you'd find planets suitable for allied races' colonists and then build them bases that would help produce fuel, ships, crew, etc., when you visited the worlds again. Due to major liberties taken with the story, most fans regard this as a missed opportunity.
SC:O looks like it's modeling itself most directly after SC2, so planetary lander minigame (now in seamless orbit-to-surface-3D!) for resource management, plus lots of alien diplomacizing and ship-blowing-up via Melee. More like SC3, it will feature a lot of original races, as Stardock doesn't own the rights to the SC1/2-era races (those belong to the game's creators), and they probably don't want to taint their game with the SC3-born characters that are so (maybe unfairly) reviled. Galactic exploration will probably be key, and light mystery solving, dialogue-tree traversal, and fleet-building-and-maintenance should all feature on some level or another.
It's also highly moddable, or at least was planned to be, so alternate campaigns, races, ships, etc., can all be slotted in by the most dedicated players. If it's as good as they said it would be a few months ago, I wouldn't be surprised to see efforts made to eventually do a Total Conversion of SC2, at least. I mean, assuming there are enough talented 3D modelers and animation riggers out there who love SC2 enough to dedicate dozens or hundreds of man-hours to recreating all the races that Stardock isn't gonna touch. . .