A way to consider the mechanism used to select features which may be divided into wrapper and filter methods. These methods are almost always supervised and are evaluated based on the performance of a resulting model on a hold out dataset.
Wrapper feature selection methods create many models with different subsets of input features and select those features that result in the best performing model according to a performance metric. These methods are unconcerned with the variable types, although they can be computationally expensive. RFE is a good example of a wrapper feature selection method.
Wrapper methods evaluate multiple models using procedures that add and/or remove predictors to find the optimal combination that maximizes model performance.