Here prussian Fusiliers of the year 1792. While the term of fusilier originally applied to soldiers armed with a flintlock musket (fusil in french), the prussian army fieled flintlocks for all troops since the late 1680s and the line infantry retained the term of Musketeer (Musketier in german) As such Füsiliere were raised as a destinct formations in 1723. Often of lesser quality than the Musketeers they were meant for the second line of battle and garrison duties.
Friedrich II. the Great tried to raise their quality, popularity and function. Thus they recieved a nicer uniform, headgear similar to grenadier caps and their function ought to be that of light infantry. In 1787 the fusilier cap was replaced by the bicorne like Kaskett hat (see pic rel).