Understanding max_features parameter in RandomForestRegressor

Straight from the documentation:

[max_features] is the size of the random subsets of features to consider when splitting a node.

So max_features is what you call m. When max_features="auto", m = p and no feature subset selection is performed in the trees, so the “random forest” is actually a bagged ensemble of ordinary regression trees. The docs go on to say that

Empirical good default values are max_features=n_features for regression problems, and max_features=sqrt(n_features) for classification tasks

By setting max_features differently, you’ll get a “true” random forest.