Futures contract - a standardized agreement between two counterparties to buy or sell an underlying asset (security, goods) at a price agreed in advance at a specified future date. The contract specifies the quality and quantity of the underlying asset. There are two types of futures: delivery and cash-settled.
The volatility index is a set of implied volatilities of a whole series of call and put options for a particular stock index. As a rule, a volatility index includes implied volatility of a stock index, but more complex volatility indices are calculated based on the implied volatility of individual shares included in the index.
A typical introductory chapter in the options textbook contains payoff diagrams that correspond to long call or long put positions. Hedging is often described as 1) simply buying a put option to protect against a decline in the price of the underlying asset or 2) buying a call option to protect against a rise in the price of the asset.