The redirect is because you had a newer version of the code than the database was run on. Koha doesn't have any support for automatic upgrades, so I guess you must have untarred 3.8.10 at some point. The version is shown in kohaversion.pl, not in file names.

You can take a look at the release notes for the versions between 3.8.5 and 3.8.10: http://git.koha-community.org/gitweb/?p=koha.git;a=tree;f=misc/release_notes;h=fd4b7d4bf8f9d401c87878ec184593a078bb5a93;hb=3.8.x

Based on the "Update report" you shared, it doesn't look like there were any actual database changes in between versions 3.8.5 and 3.8.10, but I couldn't say that with certainty without checking (you can take a look at the release notes linked above, and by reviewing the installer/data/mysql/updatedatabase.pl file on the 3.8.10 installation). The update is trigged whenever you have an older version of the database than the code, even if there aren't any database changes at all, so the fact that the upgrade run is not particularly significant. Most likely downgrading to 3.8.5 would not cause any problems at all, even if there were database changes, but it's always a good idea to check.

Regards,

Jared