C-rank and S-Rank
The S-rank is the share ranking. Your position on the share ranking is determined by the amounts of dividends you receive from owning shares in other players' companies, and how many stock points you gain from selling shares that have increased in value. See the "Stocks" help file for more details on shares.
The C-rank is determined by your company value. The higher your company value is, the higher your company ranking will be. For more details on company value, see the "Company value" help file.