Response variable can be quantitative or nominal. Predictor variables can be nominal or ordinal, and continuous predictors are supported. Number of branches equals number of categories of predictor. Number of branches varies from two to the number of categories of predictor. AID, MAID, and XAID are for quantitative responses.
FIRM comes in two varieties for categorical or continuous response.
Predictors can be nominal or ordinal and there is usually provision for a missing-value category. Some versions can handle continuous predictors, others cannot. There are also a variety of methods that do splits on linear combinations rather than single predictors. I have not yet constructed a taxonomy for such methods. Some programs combine two or more families.