Is boxed Tiger software same as install discs?

No. The Tiger package only contains OS X and only the current burned version that can be installed on all Macs released prior to that release of Tiger.

Install discs that come with a computer only contain a version of OS X specifically built for that model at the time and is not intended for use with other Mac models. They also contain the software restore archives for all the pre-installed software that originally came with the computer.

Unfortunately, G4s and G5s are very different hardware. The system you have installed on your G4 will not work on the iMac G5 unless it was made prior to May 2005. Later models require 10.4 or later. And, unless the version of 10.3.9 you have is the retail version it may not have all the hardware support required for the iMac G5.

Migration Assistant is only intended for the transfer of certain folders such as Applications, Users, for example. It cannot clone your G4 to the G5. For that you would need to use Disk Utility's Restore option.

If you are careful, it may be possible to get restore disks that would likely work for your system through ebay, but you will want to be very specific and make sure that disks you consider are made for a system of the same specs and time frame as the system you are getting them for. Otherwise, you are better off getting a retail full version of Mac OS X, but you will be lacking restore capability and the Apple Hardware Test Disk for the system. Personally, I would look elsewhere. I consider those disks like gold and never buy a system without them.

Note - even trying to be as careful as possible, doesn't guarantee the disks will work. I've seen situations where the disks were VERY computer specific, so that even similar generation and specs wasn't good enough.