an option on another underlying option, for example a call on a put

Is an option which is related to another option. A sequence on options such as a call on a subsequent call.

An option on an option.

A derivative giving its holder the right (front option) to buy or to sell another specific option (back option) for a specific amount at a specific date.

Whereby the holder of an option can purchase if they choose another specified option prior to a predetermined expiry date.