A move within the same city or 100 miles is called a local move. A long-distance move takes place outside of the city or state.
If you want to move, plan a few months ahead. From June to August, when 80% of moves happen, summer is the busiest time for moving companies. During the rest of the year, you only need to give a local moving company 2-4 weeks' notice for a local move and 4-6 weeks' notice for a long-distance move.