A derivative instrument (or simply derivative) is a financial instrument which derives its value from the value of some other financial instrument or variable. For example, a stock option is a derivative because it derives its value from the value of a stock. An interest rate swap is a derivative because it derives its value from one or more interest rate indices. The value(s) from which a derivative derives its value is called its underlier(s).
By contrast, we might speak of primary instruments, although the term cash instruments is more common. A cash instrument is an instrument whose value is determined directly by markets. Stocks, commodities, currencies and bonds are all cash instruments. The distinction between cash and derivative instruments is not always precise, but it is a useful informal distinction.
Derivative instruments are categorized in various ways. One is the distinction between linear and non-linear derivatives. The former have payoff diagrams that are linear or almost linear. The latter has payoff diagrams that are highly non-linear. Such non-linearity is always due to the derivative either being an option or having an option embedded in its structure.
A somewhat arbitrary distinction is between vanilla and exotic derivatives. The former tend to be simple and more common; the latter more complicated and specialized. There is no definitive rule for distinguishing one from the other, so the distinction is mostly a matter of custom. Usage does vary.
Exhibit 1 lists some standard derivatives and indicates the categories they fall into as stand alone (as opposed to embedded) instruments.