Yoast SEO prints an @graph whose Organization node uses home_url() + '#organization'— typically https://example.com/#organization— plus related fragments such as #website, #logo, and #webpage. The script tag is usually classed yoast-schema-graph.
Rank Math prints its own graph. Newer builds identify nodes with #schema/ patterns (for example /#schema/Organization) and a rank-math-schema script class. Even when the visible name matches, the @id is a different entity as far as a consumer is concerned.
A theme can add a third copy: JSON-LD without those plugin classes, or microdata that GraphClash will not see (we only read application/ld+json). WooCommerce can add Product (and sometimes extra Organization or WebSite) on shop URLs.
We cite the job, not fake traffic stats. If both plugins are active with schema output on, a homepage often carries two Organization nodes, two WebSite nodes, and mismatched logos if each plugin was given a different image in its settings.