The Bureau of Engraving and Printing just produces paper. Pretty paper that looks a lot like US dollars, but isn't in fact US dollars until the Federal Reserve Bank takes possession and issues it.

In any case, moneyfactory.com is just a redirect to bep.gov, so I'm not sure what the big deal is. The average person's interaction with the BEP, aside from handling paper money, is probably at their gift shop. Having a cutesy name probably made sense at some level.

It redirects to bep.gov now, but a decade+ ago it was their preferred URL.

You can still find the URL in older press releases on treasury.gov, other US government sites, and older news sites, and all I meant is that it reads very a little naïve and "off brand" to me these as a modern reader:

  https://home.treasury.gov/news/press-releases/20035137475911137 
  https://money.cnn.com/2003/09/16/pf/banking/marketing_new_money/index.htm
  https://www.dailynebraskan.com/local-businesses-prepare-for-new-20-bill/article_6a2ea77f-60e4-52aa-8217-731a6cdf9114.html

It might be parked to prevent scams

Apparently they also have moneyfactory.gov