You'll notice on the first report there is a message near the top that says:
*** FEBE was unable to load the extension data in real-time before the backup. Instead, a stored version dated 11/29/2016, 4:00:23 PM was used. Any extensions or themes installed after that date may not appear in this backup. Note that this only affects extensions and themes. All other items should have been backed up normally.
When FEBE backs up extensions, it makes an asynchronous call to AMO to retrieve a list of your installed extensions. If it cannot do this (as in this case) it attempts to use the list from the last backup. Usually the reason FEBE cannot get the list is because you are offline when the backup starts. You can manually create the list in FEBE Options > Advanced > Attempt to load and save extension data