When you add or edit a text style through the Catalog Manager, the custom text style is saved with the catalog, and is only available when editing text styles in the catalog. If you add or edit a text style when editing text in your drawing (or an element that uses text), however, the customized text style is only available in the current project when editing text styles in your drawing. The text styles library in the catalog remains unchanged. This is because the text styles library in the catalog is separate from the text styles library in the current project.
The reason that there is a project-specific text styles library is so that any text styles used in your project are always saved with the project, making it possible to share your project with others and always maintain your customized text styles.
If you want text styles that you have customized in your catalog to be available in your project-specific text styles library, or vice versa, you can use the Transfer tool to save the custom text styles to the external text styles library file (Textstyles.tsl), then import the custom text styles from the library file into the other text styles library.
Tip: You can save text styles in your template drawing by opening the template drawing, then selecting Settings > Text Styles and creating your custom text style in the Text Styles dialog. The custom text styles will then be available in the project-specific text styles library of future projects that you base on the template drawing.