Futures and options traders both trade calendar spreads, but the phrase has a different meaning depending on which type of derivative you're using.
A futures calendar spread is composed of a long or short position in the futures in one expiration cycle and a position with the opposite sign in a different expiration. Example: short one contract of February natural gas and buy one contract of April natural gas. ( We opened this position earlier in the week.) The profit or loss to a futures calendar position depends on changes in the prices of the contracts, and because the two contracts are on the same underlying asset the profitability of the spread will depend more specifically on changes in the term structure of the futures curve. In this example, if the prices of both contracts decline, but the February contract declines more, the position will make a profit.
An options calendar spread is composed of two contracts with the same underlying asset, the same right (call or put), the same strike price, and different expiration months. This sort of calendar spread is typically opened at the same time by buying one option and selling the other, e.g. by selling the at the money call in the first expiration cycle and buying the at the money call in the second expiration cycle. While a futures calendar is affected by changes in the prices of the futures contracts, an options calendar is affected not just by price changes but also by changes in implied volatility. In fact, a short calendar (sell the longer dated option and buy the nearer one) is one of the simpler ways to gain long volatility exposure using options.
Some traders think about option calendars mostly in terms of the profit potential from time decay (theta). But the gamma/theta aspects of options calendars are really only attractive if you have a forecast for realized volatility. Another reason to consider option calendars is if you have a view about the relationships among implied volatilities at different maturities. Whereas a futures calendar spread tracks changes in the term structure of futures prices, an options calendar spread is one way to trade changes in the term structure of an asset's implied volatility.