stocks tend to be more volatile than stock indices (plural of index).
Stock indices are made up of many stocks…the Dow Jones is a group of 30 stocks, the S&P 500 is 500 stocks, the Russel 2000 is 2000 stocks. Volatility is less in an index because it is a group of stocks…IE, in a hypothetical example, lets say you have an index of 2 stocks…one goes up 10%, one stock goes down 10%. At the end of the day, the index itself is little changed (low volatility). But, the stocks themselves have changed price quite a bit.
Indices enable a person to buy a group of similar things all at once. "Similar" might be many definitions: Sized companies, country, product or service, etc.
PS- there are bond indices also…and currency idices. I focused on stocks index differences because you mentioned stocks….