Stations had the most functionality, allowing the possibility of refining, repair, manufacturing, cloning, research (copying/ME/TE/invention), markets, hangers, etc.
Outposts are like smaller stations with many of the same features (markets, hangers, repair) but come in specialized flavours, for example, one has many more offices than the others while another allows refining.
Starbases (aka Player Owned Starbases) are like stripped down configurable versions of outposts, with no markets or docking but the ability to set up hangers, manufacturing, science labs, etc as can fit. In addition, they are the only platform for moon mining and moon material manufacture, and the only platform for advanced booster construction.
Citadels have added to the environment by providing competition for these existing structures by providing markets, offices, hangers, refining, repair, and cloning services. In the future, industrial arrays will arrive to take over the manufacture and research side of things, while drilling platforms will take over the moon mining activities.
We have seen how already Citadels have been used not only for markets and homes for corps and alliances, but also as offensive platforms such as the Money Badger Coalition citadels in Saranen as they try to make life hard for the Goons living there.
I predict we will see a certain synergy between Citadels and industrial structure in the future, both deployed near each other, one providing a home for the group and refining for miners, and the output minerals diverted to the nearby industrial arrays for building war materiel. Moon mining could become less complicated with a lower barrier to entry and in the future we may jump into systems to see a number of citadels, industrial arrays, and moon drilling platforms of a single alliance all working (and defending) together.
How all these pieces will truly fit together depends on a lot of details of course, but I look forward to seeing it happen.
And of course, what those promised stargates will do.