You can use your muzzleloader during firearms season as long as you have a firearms license. But you must also have a muzzleloader license if you hunt with the muzzleloader during muzzleloader season.
MZ (and other equipment) used to be tag specific for gun season. But if you didn't fill your MZ tag during firearms it would carry over to the later primitive season.
That changed long ago.
Now our firearms season is "consolidated". To hunt the late MZ season, you have to buy an MZ tag (if not using bonus).
Heck, way back I remember buying a shotgun tag and a handgun tag.............all for a chance at a buck during gun season.