American options can be exercised at any time prior to expiration. If some of the available expiration periods are restricted, then it becomes a nonstandard option. Restricting early exercise to certain dates is known as a Bermudan option.
Binary options generate discontinuous payoff profiles because they pay only one price at expiration if the asset value is above the strike price. Chooser options allow the owner, after a certain period of time has elapsed, to choose whether the option is a call or a put.
