What you are mostly seeing is the difference between mobilization before the formation of the modern National Guard, and after it.

For the first 150ish years you would have the small Regular Army of professionally trained officers and volunteers who would man forts on the coasts, and the frontier and serve as the core of any force in the event of war. And the regiments and battalions that made up this small force were named and numbered in a conventional way, 1st United States Infantry, 2nd US Dragoons, etc.

But when war came this force would be supplemented by far larger contingents that were raised individually by the states. Typically in numbers and ratios allocated by the federal govt, so NY would raise 10 regiments, PA 8, DE 2, etc for a length of service determined in accordance with the need, but could range from 90 days, to 12 months, to 3 years, to the duration of the conflict. The state governments would then fill out these units and control the appointment of their officers and they would then report to a designated camp and after fitting out and inspection would be accepted into federal service and shipped out to the war. Sometimes states would raise extra units of volunteers or local militia into active service that might be accepted into Federal service or meant to be retained under state control for local defense as well.

These units would then typically be named with their state and type and numeric designation, so the 1st New Jersey Cavalry, or 69th New York Volunteer Infantry, etc.

And while this system could work, and reached a relatively effective level in the Civil War, it had several drawbacks. Namely that the federal govt had relatively few controls over the states conduct as it related to the units. Especially in areas like training men in peacetime, organization of contingents, and appointment of officers.

The last conflict where this system was sued, and its faults on full display was the Spanish American War of 1898. In 1903 the Dick Act was one of the early serious reforms of this issue, in exchange for more federal funding for their militia/volunteer units, the expectation of annual training and a standard of professionalism in state units was set.

Then in 1916 comes the major change in the National Defense Act of 1916. This established essentially the National Guard as we know it today, it allowed the War Department to say what size and what type of units each state would be required to maintain in peacetime, set a budget for the units, and also established ROTC to provide for a body or officers for a mobilizing force.

It also forced the renaming of virtually all units in the new National Guard as the state designations were now not needed, however even today many Guard units retain the memory and legacy of state units some dating back even to the Revolution!