Correct, $200 tax plus forms and a background check on each item. In Texas we can hunt any non game animal with ANY weapon that is legal to own. Non game animals are varmints like coyote, hogs, racoon, armadillo, etc... These animals can be hunted with a silenced machinegun if you want, or a GE Minigun.
For maximum sound reduction you need the projectile to be sub sonic (below the speed of sound) which is about 1100 fps. So for maximum hunting power you want the biggest heaviest projectile since all the projectiles must be around 1050 fps. This is why a 44 mag is more desirable than a 357 mag. Some people use super long and heavy bullets in other calibers like 300 whisper, but then you need special fast twist barrels to stabilze. The 44 mag handi is at a slight disadvantage due to the 1-38" twist compared to most other 44 mag rifles that use much faster twists.