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Hello @generosus,
Thank you for contacting Rank Math support.
The on-site analyzer has some additional tests that include focus keywords, search engine visibility settings, permalink structure, GSC connection, etc., and that’s why there can be a difference in the scores of on-site analyzer and external analyzer. If you notice, there are 21 tests in the RankMath.com version and 29 on the on-site version. Some of the additional tests are only possible when the plugin has access to additional backend data.
Hope that helps and please do not hesitate to let us know if you need our assistance with anything else.