I wouldn't delete the older version. Chances are that you only have one version installed. The Windows Registry is probably screwed up a bit and is showing the two versions incorrectly. Not unusual for that to happen with Windows, but it ain't hurting you in any way.

If you are comfortable with using the registry editor then you can inspect and delete the orphaned entry for the older Firefox version.

If you have a 64 bit Windows version then inspect this key:

HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall\Mozilla Firefox  (????)

Thanks to both of you! I found the registry entries but was not comfortable deleting them. Will explore that option some more. Thank you!

This worked for me... I also have an old version of Mozilla Maintenance Service that shows in the registry at the same place. Can I just delete that as well? There are 1 year old files at the location indicated by the registry - perhaps if the current version is not 38.0.1 I should actually uninstall it?

Is the current version of Mozilla Maintenance Service 38.0.1 ?

The installed version of Mozilla Maintenance Service should always be the version that comes with the highest Firefox version that you have installed now or in the past. This can be complicated if you have installed developer versions like Beta or other update channels. There should also be one Mozilla Maintenance Service installation folder.

If there are multiple version listed in the uninstall registry then should should verify that they point to separate installation folders. In a lot of cases you only see orphaned registry entries that weren't removed with an update.