Vanguard also has a neat Monte Carlo retirement simulator that runs 5,000 simulations of an initial investment with a given stocks/bonds allocation using random (non-Markovian) historical data

So, it randomly samples from the empirical distribution? That's not a good idea, returns (especially of bonds) have time-series structure which should not be ignored. And what about asset class correlations?

All such simulators essentially specify a model of the market(s). Before taking its results seriously you should think about the underlying model and how adequate it is (usually not very).

So what do people mean by "risk"?

This is a very long discussion, several book-lengths long. There are multiple definitions, from precise but not always helpful (e.g. "sample standard deviation") to intuitive but not very useful (e.g. "the chance of bad things happening"). The two main varieties are some more or less symmetric measures of variance (e.g. volatility), and specifically asymmetric measures of the left tail (e.g. VAR, value-at-risk).

"People giving investment advice" are, as usual, acting according to their incentives. I recommend figuring out what their incentives are.