Library databases are collections of information that you can search. Library databases contain scholarly journal articles, magazine and newspaper articles, reports, and much more that often is not available freely on the Internet. That's because much of the materials needed to do proper research are behind paywalls. The library helps you by giving you access to these materials through databases.
A library catalog is a collection of items that your library owns or subscribes to. It is best for looking up books and eBooks or to check if your library subscribe to a particular journal or other periodical (like a newspaper or magazine). It will not give you the same level of detail about articles that you can find in a library database.