YUI Doc is the more common of the two in our index: it runs on 157 websites against 6 for Read the Docs. Counts come from real scans, not vendor claims.
Read the Docs is a documentation platform that uses a Docs-as-Code workflow to provide versioned content, integrated previews, and secure authentication directly within standard Git development processes.
YUI Doc is a Node.js application used at build time to generate API documentation.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.