The mission is the same. The crew of the U.S.S. Enterprise, the flagship of the Federation, sets forth to explore new worlds and make contact with as many new civilizations and life forms as possible. Only this time, the ship and its crew are both considerably larger, and the technology that is both possessed and faced is naturally more powerful as well as more complex.
The show aired for seven seasons during which time Gene Roddenberry passed away, but the tradition was quite ably carried on by Executive Producer Rick Berman with help from some cast members who were given oportunities to write and direct episodes.