Things like Black-Scholes (using past volatility of the underlying to model the probability distribution in the future) are often used by market makers to price options, but the vanilla version never is.

Any market maker pricing options with Black-Scholes won't be a market maker for long.

Black-Scholes is just a customer-facing description of the option (i.e, it provides greeks that everyone can understand). But it isn't used as a starting point.

In practice, MM will back out what the implied volatility is from current prices. Then a stochastic volatility model is calibrated against that.

https://en.wikipedia.org/wiki/Stochastic_volatility

No - no market maker is using stochastic volatility. (L)SV is only used for exotics. Market makers use a tricked out Black Scholes where the 'secret sauce' is in how you apply the chain rule when you calculate the greeks.

Would be curious to know more about this.