TinyCat is designed for “tiny” libraries (collections of less than 10,000 titles) while LibraryThing for Libraries is marketed to public and academic libraries.
From the Blog Post:
These smallest libraries—churches, synagogues, small schools, community centers, academic departments, etc.—have been using LibraryThing to catalog their collections for almost a decade. That continues with TinyCat. TinyCat offers a new way to view the catalog that’s cleaner and focused on helping patrons find and discover books in your library.
Ed. Note: Smart move in our view for LibraryThing to develop an online catalog solution for a specific type of library, in this case small/tiny collections. We look forward to seeing TinyCat while in San Francisco.