If you select a scene and export a package with it including dependencies, the terrain should come along, along with all of the terrain's assets (trees, etc.).
The TerrainData object in the Project view should contain all of the basic information (splat maps, trees, details, etc.
The Terrain instance in the Scene Hierarchy points to that terrain object AND has the runtime settings like billboard distance, etc. in it. So those things will only be copied if the instance is copied between scenes.