1 - General rule about catalogs (not only Elements, but also Lightroom and other third-party management softwares based on catalogs):
What you do in a catalog is ignored in any other catalog, even of the same software, the same version.
2 - "albums", also called "collections" in old Organizer versions or in Lightroom are just lists of pointers to files managed in the catalogs. Think of them just as "playlists". Albums don't contain any media files, only sorted lists of items managed in the catalog. They are not like keywords either. Those keywords can be saved (written) in the metadata header of the media file. Albums are only stored in the catalogs.
3 - Including a given media file in several different albums for different purposes is quite possible. Each list points to the same media in the catalog without creating any duplication.
So, copying or moving albums from a catalog to another one is meaningless. What is possible is to manually create a similar album (list) in the target catalog. Keep in mind that if you move, rename or delete a file from one catalog, that will not be reflected in the other catalog, with the result of missing / disconnected files. You can delete a file from the list, keeping it on your computer, then the second catalog will not be affected.
You can make creating a similar album in another catalog easier. For instance, you can select the files of an album and move them all to a new subfolder from which you'll import in the second catalog and you'll create an album from the import batch. Still many traps in that situation, for instance if some of the files are already in the destination catalog...
The lesson is that there are good reasons to use a single catalog instead of splitting it into many smaller ones. With a single catalog, it's easy to create a new album from an existing one. You can change which files are or not in different catalogs. However, you'll have to take care not to delete files physically from disk in an album, this will affect the other albums including them. If you rename or move files from an album, that will be automatically reflected in other albums.
Another way to manage similar albums in two different catalogs would be to "export" the files of an album and re-import them. You would create voluntarily duplicates, but that would insure the independence of edition from different catalogs.