As others have said 'championship' is usually the name of a competition. The 'final game of the season' means the last game of a league competition in football (where every team plays each other twice). However there are lot's of 'finals' for different competitions where two teams play each other to decide who wins. It gets confusing because in European football there is 'the Championship', which is the second league in England (below the Premier League) and the 'Champions League', which is the ultimate competition for the best teams in Europe. So here you would have 'The Champions League Final' and 'the final game of the Championship'.