In statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished:

The distinction between these last two classes is not consistently made; Jebara (2004) refers to these three classes as generative learning, conditional learning, and discriminative learning, but Ng & Jordan (2002) only distinguish two classes, calling them generative classifiers (joint distribution) and discriminative classifiers (conditional distribution or no distribution), not distinguishing between the latter two classes. Analogously, a classifier based on a generative model is a generative classifier, while a classifier based on a discriminative model is a discriminative classifier, though this term also refers to classifiers that are not based on a model.

Standard examples of each, all of which are linear classifiers, are:

In application to classification, one wishes to go from an observation x to a label y (or probability distribution on labels). One can compute this directly, without using a probability distribution (distribution-free classifier); one can estimate the probability of a label given an observation, ${\displaystyle P(Y|X=x)}$ (discriminative model), and base classification on that; or one can estimate the joint distribution ${\displaystyle P(X,Y)}$ (generative model), from that compute the conditional probability ${\displaystyle P(Y|X=x)}$, and then base classification on that. These are increasingly indirect, but increasingly probabilistic, allowing more domain knowledge and probability theory to be applied. In practice different approaches are used, depending on the particular problem, and hybrids can combine strengths of multiple approaches.

An alternative division defines these symmetrically as:

Regardless of precise definition, the terminology is constitutional because a generative model can be used to "generate" random instances (outcomes), either of an observation and target ${\displaystyle (x,y)}$, or of an observation x given a target value y, while a discriminative model or discriminative classifier (without a model) can be used to "discriminate" the value of the target variable Y, given an observation x. The difference between "discriminate" (distinguish) and "classify" is subtle, and these are not consistently distinguished. (The term "discriminative classifier" becomes a pleonasm when "discrimination" is equivalent to "classification".)

The term "generative model" is also used to describe models that generate instances of output variables in a way that has no clear relationship to probability distributions over potential samples of input variables. Generative adversarial networks are examples of this class of generative models, and are judged primarily by the similarity of particular outputs to potential inputs. Such models are not classifiers.

In application to classification, the observable X is frequently a continuous variable, the target Y is generally a discrete variable consisting of a finite set of labels, and the conditional probability ${\displaystyle P(Y\mid X)}$ can also be interpreted as a (non-deterministic) target function ${\displaystyle f\colon X\to Y}$, considering X as inputs and Y as outputs.