Fowling pieces which varied a lot but were designed for hunting were often converted to musket use by cutting back the fore-end and attaching a lug for a bayonet. Then they met militia requirements, while belonging to individual civilians.
On the other hand, muskets, usually made to a pattern, being heavier in general and made for shooting round ball, could be used to shoot birds but would be pretty clunky. Plus they belonged to the state, or colony, or crown. Generally, military arms remained with the military.
So in general, a fowling piece could serve as a musket for a militia man, but a musket would be a poor fowling piece and civilians would not normally own one except to meet militia requirements.
Then there are trade guns, but let's lump those with fowling pieces.