Both the words federal and national are very similar because they refer to the whole country in respect to the noun it modifies. The difference between the federal government and the national government is based upon their definitions. The word federal means controlled by the group of states. National means pertaining to the country. It seems that there is a fine line between the meaning or use of the word federal or national government.
However, national means if you are referring to the country as a whole and the federal refers to a group of states. Federal comes from the word federation which refers to a group of something acting together. In most cases, federal government is referred to in the United States when discussing the government in Washington D.C.