Is there any reason why Time Machine only finds my NAS over wifi? I've got a 2009 MacBook Pro running OS X 10.5.7 and a Synology Diskstation ds215j.  I've successfully set up a user for Time Machine on the NAS and have successfully performed backups.

However, this only works over wifi!  When I connect [my Mac] to my router via Ethernet cable, Time Machine fails to find the disk.  Both DHCP addresses (wired and wireless) are on the same subnet, which is the same subnet as the NAS.

Can anybody tell me why?!
I believe the issue you are referring to is the fact that the only drives that you are allowed to use as a time machine are ones that are internal to a Apple router, the only way for this to work is if you had an Airport Time Capsule which has a built in hard-drive. That is the only drive Time Machine supports connected to your router. 

Basically you CANNOT use a drive hooked-up via ethernet to your router for Time Machine. You have to have a Airport Time Capsule and use the internal hard drive. That is why when you connect your NAS Time Machine does not recognize the drive.