I'm sorry, but that's pretty much a no-brainer design choice.
- The square is the most obvious choice of shape in which to contain text.
- Blue is used for everything these days, as it's easy to see and calming, and the government is no exception to this design trend.
- The division of the domain name from the domain suffix is likewise obvious. It's following the rule of maximum readability, breaking text into a square-like shape rather than a single string. The traditional suffixes, .com, .net, .gov, and .org, are all three letters by design, so it's not surprising that two short URLs would end up looking the same.
- Finally, one difference is that the JW logo uses a simple, sans-serif font and the White House uses a distinguished looking serif font.