The usual calendar spread, also called a time spread or horizontal spread, involves the purchase of options of a named striking price expriring in a more distant month and the sale of options having the same striking price that expire in a more nearby month.
The calendar spread is a strategy used by the trader in an attempt to take advantage of a difference in the implied volatilities between two different months' options. The trader will ordinarily implement this strategy when the options he is buying have a distinctly lower implied volatility than the options he is writing (selling).
In the typical version of this strategy, a rise in the overall implied volatility of a market's options during the trade will tend very strongly to be to the trader's advantage, and a decline in implied volatility will tend strongly to work to the trader's disadvantage.
If the trader, instead, buys a nearby month's options in some underlying market and sells that same underlying market's further-out options of the same striking price, this is known as a reverse calendar spread. This strategy will tend strongly to benefit from a decline in the overall implied volatility of that market's options over time.
A calendar spread may be implemented using either call options or put options, but never with calls and puts used together in the same trade.