I looked at some of the government web sites that I have been using for info and this is what I found:
from usembassy.state.govThe federal government of the United States consists of three parts:  the executive, legislative and judicial branches. The ...
from www.info.govDescribes the basis of the government of the US ... Federal, State, and local governments are explained and compared. 
Those sites make a distinction between the government of the United States being all three versus the federal government being just well, the federal government. BTW: In the Politics section, you'll find a general description of the state and local govs, again taken from the usinfo.state.gov site. -