As I already said, Hosta kikutii var. yakusimensis is a synonym. We do not have separate entries for synonyms because they are obsolete names.
http://www.catalogueoflife.org...
Your links are dated 2008 and 2010. Mine is dated 2018 and shows that the latest taxonomic scrutiny was performed in August 2017.
If the Catalogue of Life changes the classification of these names in the future, our database entries will be updated to reflect these changes.