In simple words:
- tags (or keywords, that's the same) are text properties you assign to a given media file. Generally, you assign several keywords to a given picture file for easy retrieval by combining the keywords. You can assign the same keyword to a number of selected files at the same time. The keywords are managed in the catalog (the database) and you can also 'write metadata to files' so that they can be seen from any other softwares without the catalog.
- albums are not properties of a given file, they are simple lists like playlists for audio files. They are only kept in the catalog and are a way to group files for a given purpose. They are NOT like folders. You can include a photo in several different 'albums' for different purposes, there is no duplication of the file itself; the photo included in several lists is the same. If you change it from the selection of one album the changes are seen from any other album.
In practice: you should work mainly with keywords and create albums for a given purpose: showing, printing, sharing. Most users create many temporary albums for their current purpose and deleted those lists afterwards. The big advantage of those lists is that you can sort the list in your own custom order 'album order'.
The advantage of keywords is that you can write them to file if you want to share them with other softwares (or different catalogs). It may be an additional safety beside backups.