Musket: A smoothbore long barreled arm, and on the majority of these they lack a rear sight. Examples would be the Model 1816 and Model 1842 which both had 42" barrels and no rear sight.

Rifle: A shorter barreled arm with a rifled bore. The Model 1841 "Mississippi" rifle is a good example, having a 33" barrel as well as front and rear sights.

Rifle-musket: Of musket length but originally made with a rifled bore. The 40" barreled Model 1861 Springfield is an example, which also has front and rear sights.

Rifled-musket: Started life as a smoothbore musket but has been upgraded by having the bore rifled and sometimes (but not always) having a rear sight installed. A Model 1842, which you might see referred to as "rifled and sighted", is a good example.

Although this terminology is "correct", you will not always find it properly applied in Civil War era correspondence, by modern historians, nor present
day collectors, myself included :)

JHG