In military service, there were certainly standard patterns of musket throughout much of the 18th and early 19th centuries; famously, the British Land, Short Land, and India pattern muskets collectively known as 'Brown Bess' were a series of similar musket patterns used by Britain (and exported to its allies) from the 1740s to the adoption of rifled muskets in the 19th century. France standardised a rough pattern in 1717 and kept it until around the same time the British moved to rifled muskets. Other European (and, indeed, American) nations all had musket patterns.

However, it's important to remember that a pattern is not the same as a standard. Generally, while each musket would be made to the same specifications, there was no interchangeability of parts, nor a particularly exacting set of standards. The most important point, generally, was that the standard calibre of musket ball fit down the barrel. However, these muskets weren't really available on the civilian market; while it'd probably be possible to get hold of one, most weapons were the property either of the Army or of a unit's commanding officer, and therefore weren't likely to be sold for profit. In general, someone wanting a musket outside the army would turn to a gunsmith to make one - and probably better than the State arsenals could.