There isn't a built-in way to extend the text search value to content type-specific fields (like a "description" field). Currently, the search only works against the "common" fields, preventing the requirement for a massive SQL JOIN across all content type-specific tables in the database.
My recommendation - use one or more taxonomy fields for all content types.
These taxonomy fields can be used for internal content discovery and organization of content in the Content hub using filters and smart folders, drive external customer experiences, or both.
If search across all fields (or many content type-specific fields) is a requirement, you'll want to build your own search experience in the Admin UI using a search technology, not SQL Server. You could try using our Lucene integration for this.