There was also the National Guard and Reserves. These could be called up in the event of war. There was no need of a large standing army, as it was almost impossible for the US to be invaded without a long warning period. The US had maybe the number 2 or 3 navy at that time. The size of the army led foreign power to underestimate the military power of the US.
The British colonies in North America originally had a militia system, in which every single free man was legally required to own a musket and ammunition, and to periodically drill with the other men of his locality. In time of war, the militiamen would be required to fight. Every British colony, and every state and territory in the United States, had its own separate militia system. And the Federal government of the USA could cal on the states to furnish militia for a war. But during the early days of the USA the militia laws began to be less and less enforced and fewer and fewer men would show up for drills which took places less and less regularly. The militia was still used in wars up until the US Civil War but became much less militarily efficient and significant.
The Militia Act of 1903 reorganized the militia and more or less created the National Guard, a system of joint State and Federal control and support of the militia. The USA has separate National Guards for all 50 states and 4 territories, which are also part of the federal National Guard of the United States created in 1933. Some states have Air or Navy National Guards in addition to Army National Guard. Members of the National Guard are civilians with civilian jobs who can be called up by their state government when needed in the state or by the federal governments when needed, including outside the state and outside the USA.
Many National Guard units were formed as militia units before the Militia Act of 1903, in the 19th, 18th, or 17th centuries, the oldest units being formed in 1638.
Almost every state has laws authorizing a state defense force, and 22 states currently have active state defense forces separate from the National Guard.
The Continental Line During the Revolutionary War was more or less a standing army but was demobilized in 1783, and the standing army of the USA was founded in 1784, 5 years before the federal government under the present constitution. The standing army of full time professional soldiers is called the regular army or the United States Army. Up until about 1900 the main jobs of the regular army were policing the Indian frontier - fighting Indian Wars when they happened - and manning coastal defense forts. During the 18th and 19th centuries the regular army was always too small for the tasks it was given.
During 19th century wars when the federal government needed a lot more soldiers, it would expand the regular army, use state militia units whenever possible, and formed units of United States Volunteers, full time soldiers in units that lasted for the duration of the war. Men who volunteered would be organized into units by their state or territorial governments and company and field level officers would be appointed by the state or territorial governments. It was possible for a state government to pay for a volunteer unit but most volunteer units were mustered into federal service and paid and supplied and equipped by the federal government. Volunteer units were usually designated by their state or territory and by number, but were collectively called the United States Volunteers.
The majority of United States Volunteers were volunteers. During the Civil War a small percentage of the soldiers were drafted, and there was no more conscription until World War I. During World War I the regular army, mobilized National Guard units, and millions of drafted men were combined into The National Army, which was disbanded in 1920. In World war II the Army of the United States was formed, combining regular army, National Guard, conscripted soldiers, and Reserve forces. The Army of the United States still legally exists but has been inactive since the suspension of the draft and switch to all volunteer forces in 1973.
The United States Army Reserve was created in 1920 in the National Defense Act that organized the US land forces, into the Regular Army, the National Guard, and the Organized Reserve. Reserve soldiers are civilians like the National guard with civilian jobs but are periodically called to full time duty.
This site gives numbers of US armed forces members from 1789 to 1997. I think that army figures include regular army (United States army), United States Volunteers, Reserve units on active duty, National Army, and Army of the United States, but not militia, or National guard not on active duty or Reserve units not on active duty.
U.S. Military Manpower - 1789 to 1997