A calendar spread (time spread) refers to selling a near term expiry option and buying a longer term expiry option, at the same strike
This strategy can be done with either calls or puts.
Since expiry is not at the same time, the payoff diagram does not exist. Instead, you will need to understand this position using the greeks.
When the calendar spread is ATM, the long calendar is
1. Option value is purely extrinsic
2. Short Gamma
3. Long Vega
4. Collecting Theta
When the underlying moves and the strikes become further out of the money, then the greeks could change. In particular, if the near term option becomes nearly worthless, then the calendar spread is essentially a long option trade. Hence, it becomes
1. Long Gamma
2. Long Vega
3. Paying Theta
This illustrates that the greeks of the position are greatly subject to change, especially if the near term expiry is close to expiration.
This trade greatly depends on the volatility term structure, and what you believe will happen to it. You have to be extremely careful with a calendar trade, because there are more unknowns, which could affect your position.
Consider buying a calendar spread in the following situations:
1. Volatility in the front month is too high, and so you sell it while buying the back months. Note that while it's possible to be long gamma and collecting theta (due to the bad Gamma Theta Ratio), you can lose a lot of money when volatility comes off because the back months have a lot more vega.
2. You believe that the near term movement is over-hyped and going to be a non-event.
3. Volatility in the front month is too low, and there is potential for movement (perhaps due to market instability).