Hrmm .. this is sort of a complex issue with many facets. To start off, numerical regimental designations were usually used only when more than one regiment of that sort existed. Thus, the Delaware Regiment didn't need a number because it was the only regiment from Delaware. To further confuse, some regiments were known by both a numerical designation and by the name of its commander. Thus, the 4th Continental Artillery Regiment was also known as Proctor's Artillery Regiment. Occasionally, a regiment retained a former commander's name after he'd been killed; for instance the Delaware Regiment was also known as Haslet's Regiment and continued to be called that well after John Haslet had been killed at Princeton in 1777.
Operationally, the distinction between state and Continental regiments was important. Continental regiments were part of the Continental Army establishment had to comply with the orders of Continental officers. State regiments were less constrained by a responsibility to national authorities. Most were directed by their respective states to cooperate fully with the Continental Army, often subordinating their own command to Continental command. However, there are notable exceptions, like the New Hampshire militia under John Stark who refused to support Schuyler at Saratoga.
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When a regiment passed into Continental service, this transfer was recorded in government and military records. For instance, we know that on June 6, 1777, the Pennsylvania State Regiment was offered by Pennsylvania authorities to Congress for incorporation into the Continental Army. On June 10th, the Continental Congress accepted the offer and the regiment was transfered. Within a few weeks, the regiment had unofficially taken on the name "13th Pennsylvania Regiment." And on November 12th, the numerical designation became official.
Interestingly, there seems to be a species of military unit that is often overlooked by historians and not really acknowledged in the BG! rules. The Pennsylvania State Regiment (prior to its incorporation into the Continental Army establishment) seems to have occupied a space between militia and Continental Line regiment. It appears to have been like a Continental regiment in strength and its condition of permanent activation, yet still a state controlled unit with restrictions on where it could operate (i.e. inside the state of Pennsylvania) and some consequential freedom from national authority. The PSR was a fully-formed professional regiment of national calibre, but for Pennsylvania exclusively. I don't know much about the Green Mountain Boys, but perhaps they were similar? Surely there were other state units that occupied a similar position.
Er, sorry. Perhaps this explanation is more nuanced than you need.