Light sources are basically light bulbs. They are applied to light fixtures. When you add or edit a light source through the Catalog Manager, the custom light source is saved with the catalog, and is only available when editing light sources in the catalog. If you add or edit a light source when editing a light fixture that has been inserted in your drawing, however, the customized light source is only available in the current project when editing the properties of inserted light fixtures. The light source library in the catalog remains unchanged. This is because the light source library in the catalog is separate from the light source library in the current drawing.
The reason that there is a project-specific light source library is so that any light sources used in your project are always saved with the project, making it possible to share your project with others and always maintain your customized light sources.
If you want light sources that you have customized in your catalog to be available in your project-specific light source library, or vice versa, you can use the Transfer tool to save the custom light sources to the external light source library file (Lights.llb), then import the custom light source from the library file into the other light source library.