There are more regulations for having an outdoor fire pit than target shooting in your backyard

When I wanted to burn debris (downed tree limbs, invasive vines, and brush) from around my small piece of property I had to schedule an inspection from the town's fire marshall. The marshall came out and inspected the location and materials used to construct the fire pit. I was then instructed that burning was only allowed when wind speeds were below a certain amount, humidity had to be above a certain amount, and the state wide fire ban had to be categorized as low or lower. Then I had to call the town's dispatch phone number and report that I was going to burn. Dispatch would verify the weather was amicable for burning and that the Fire Marshall's fire danger rating (which differed from the state) allowed burning. If all this checked out then I was allowed to burn but only between certain hours.

If you want to shoot in your backyard you literally do not have to do a thing other than load, aim, and pull the trigger. Nearby hiking trails? Who cares... Will your bullets leave your property and travel across numerous other property lines? No one cares. Nearby school? Yea, you guessed it no one cares.