The Black-Scholes-Merton model (BSM) is the fuller name of the Black-Scholes model, the standard formula for valuing a European option. The two names refer to the same framework, and the main entry sets out the formula, its assumptions and its limits. The longer name credits Robert C. Merton, whose 1973 paper appeared in the same year as the paper by Fischer Black and Myron Scholes.
Merton's contribution was more than a restatement. He derived the result using continuous-time mathematics and a no-arbitrage argument in which the option is hedged continuously with the underlying asset. He also extended the formula to shares that pay a steady dividend yield. When writers wish to be exact, "Black-Scholes-Merton" often means this dividend-adjusted version, and "Black-Scholes" the original for a share paying no dividends.
Scholes and Merton received the Nobel Memorial Prize in Economic Sciences in 1997 for the work. Black had died in 1995 and the prize is not awarded posthumously, though the committee noted his role. The model remains the usual starting point for quoting implied volatility and computing the option Greeks.