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A federal census is a great way to find out all kinds of historical information about our country in great detail, especially during the late 19th century. There is no difference between a "US census" and "US federal census" besides the simplification of the former name. The census was always undertaken by the government due to the sheer size and scope of the project. In looking for information on the 1890 census you request, I found two things of value. The first you might have already known is that a large part of this census was destroyed by fire in 1921 in the Commerce Building in D.C. The part that was lost was most of the population schedules. The second thing I found is a website with PDF files of the 25 volumes of the final report, abstracts and compendium and supplementary reports. That site is: http://www.census.gov/prod/www/abs/decennial/1890.htm
These final reports will not give in-depth information about households, as it sounds like you want. The remaining information that survived from the fire can be found here:
While there are only a few bits of family information remaining, maybe you'll get lucky and find yours! I hope this is helpful, good luck in your research!