A "commercial spacecraft" refers to a privately-owned and operated spacecraft that is used for business purposes, like transporting goods or people to space. It is not owned or run by a government or a space agency. Full definition
What the hell would an efficient commercial spacecraft be like? (businessinsider.com)
The BAA solicited proposals for studies in five key areas: asteroid capture systems, rendezvous sensors, adapting commercial spacecraft for the Asteroid Redirect Vehicle, partnerships for secondary payloads, and potential partnerships to enhance U.S. exploration activities in cis - lunar space in conjunction with the crewed mission. (sciencedaily.com)
SpaceX's trial run back in May was successful, making Dragon the first commercial spacecraft to dock with the ISS. (newscientist.com)