I was wondering the same thing, after digging a little bit I found this FAA page:
What qualifies as a commercial launch?
What is a commercial launch?
The Federal Aviation Administration (FAA) Office of Commercial Space Transportation (AST) defines a commercial launch as having one or more of the following characteristics:
The launch is licensed by FAA.
The primary payload's launch contract was open to international competition.
The launch was privately financed without government support. Commercial launch vehicles are manufactured and marketed by private companies.
FAA's launch regulations require a license or a permit for all commercial launches taking place within U.S. borders as well as for launches being conducted abroad by U.S. entities. In general, FAA does not license launches by U.S. government organizations. In addition, certain classes of small rockets are exempt from licensing requirements.
As far as getting a launch license, the process is quite long and complicated. Link: https://www.faa.gov/space/streamlined_licensing_process/licensing_process/
https://www.govtrack.us/congress/bills/98/hr3942/text This, about the Commercial space launch act (U.S.), details many laws and regulations.
I believe there are a lot more restrictions for commercial use than for private use, and as far as launching deep space objects, I don't couldn't find anything about that, but you should keep digging.
I hope this answers your questions