1)It does have a campaign. Sort of. It's basically a huge world map with various theme park locations you can buy. The goal is to get each park to a certain value and then sell it for enough profit that you can buy a more expensive plot of land. At the beginning, you only have one location to choose from and all of them vary in terms of conditions and difficulty.

2) The game is a somewhat extensive campaign (I think 10 or 12 consecutive missions). It continuously increases in difficulty and complexity. Each mission introduces new mechanics, diseases and rooms to build and it really gets crazy after a while.
Usually, the mission goals are "cure X amount of patients" and "raise Hospital value to X amount of dollars".

3) It's a management game, there isn't really a story to speak of outside of "do things, get money".
They're not even very similar in terms of gameplay. Theme Park is a pretty typical business management sim with a sense of humour, as well as a good bit more personality and less refined gameplay than Rollercoaster Tycoon; whereas Theme Hospital plays a lot more like Dungeon Keeper, with a focus on various rooms to place and manage in a very confined space and staff members that you have to keep happy while they do their job.
Theme Hospital is also a hilarious game, with a pretty dark sense of humour.