I thought there was almost no difference, but to be exact, there is.   In kanji, it may be easier to understand the gap.

　Shogun is usually translated as “generalissimo.” It was originally a temporary title given by the emperor to the commander-in-chief of an expeditionary army.   　Later, it developed into the official title given by the emperor to the administrative head of the country. The rule under the dictatorship of the shogun lasted until the mid-19th century. […]