Xrite i1 Studio sells for 365€ to 400€ in Germany.
Calibrite ColorChecker Studio sells for 500€.
What am I missing? Any difference in box content I may have missed?
No, I don't think that you're missing anything. It's just rebranding the product; distribution and support thru a different channel; and the price increase which you've noted. You can currently save money by buying the X-Rite branded product.
Over the years, it seems every effort has been made to keep customers as confused as possible thru the use of similar product names for different hardware products; multiple packaging for the same hardware with different software; and changes in branding for the same product. Whether the spectrometer device is branded as X-Rite, Pantone, or Calibrite it's the same device. This also applies to whether the spectrometer model is called ColorMunki, i1Studio, or ColorChecker Studio—they are all the same spectrometer hardware.
Here's a
YouTube video from Calibrite explaining the switch in branding which I've set to start at the X-Rite i1 Studio/Calibrite ColorChecker Studio portion.