I searched for updates using the update manager. It found updates for Entity and Rules. I used the automatic method for updating these two APIs. When I tried to navigate back to my website, I was told that the site could not find an include file for Rules. I looked at the directory under SSH, and I found out that Rules had been installed to sites/all/modules/rules/rules instead of sites/all/modules/rules. After I fixed that, I found out that Entity had been installed to sites/all/modules/entity/entity instead of sites/all/modules/entity. In both cases, Drupal was looking for files in sites/all/modules/X and not finding them because the updated files had been in stalled in sites/all/modules/X/X. This suggests this is a problem that is generic (the update manager) and not specific to the packages.