Yes, it is definitely a "ball button." They were sometimes also referred to as a "bullet button" in Military Regulations for uniforms.
Insofar as I'm aware, they start showing up during the latter 1700s, in European armies. They came to the American colonies with the British. They were used on early US Army uniforms. The Albert button-book says "The earliest reference to the buttons worn by officers of the [US Army] General Staff is dated 1810: 'All officers of the General Staff ... single-breasted coats, with ten yellow gilt bullet buttons.' They continued to be the Regulation button for such officers until 1832.
These "ball buttons/bullet buttons" were also used on local Militia uniforms. A goodly number of them have been excavated from American civil war battle and campsites. Many military-schools have used them on cadet uniforms, even long after they were discontinued for US Army use. Last I heard, they are still in use today on Virginia Military Institute cadet uniforms. Which is why the Waterbury Button Company is still manufacturing them.
