I've seen some different boxed versions of Fritz 13 (and 12 for that matter). What's different in the boxes?

The prices are different so I assume the software is different. But in what way(s)?

I have the Chessbase verson (your first pic) of Fritz.  And judging from the screenshots of the "Games For Windows" version (your second pic) on Amazon here: http://www.amazon.com/Viva-Media-V01001-Fritz-Chess/dp/B00604IFBQ   it appears to be exactly the same as mine.  The Chessbase version looks like it comes with a 6 month "Playchess" membership though, whereas the "Games For Windows" version only comes with 1 month. 

I'd still get it from Chessbase though, there's might be alot more hoops to jump through trying to troubleshoot issues with the "Games For Windows" version via Chessbase and they try and say "That version isn't published by us, sorry we can't help you blah blah".  And also, I'm not familiar with who the "Viva Media" publisher is on your second pic, and highly doubt they have an interest in Chess other than to profit from the Fritz name.  Chessbase is actually a part of the chess scene and contributes quite alot.  Go with the Chessbase version.