Generative models learn distributions in [[generative space]].
Discriminative models, in contrast, learn decision boundaries to discriminate between predictions or classifications based on data distributions.
In terms of probabilities, the generative model is concerned with predicting $X$ given some label $y$ as in $P(X | y)$ whereas the discriminative model is concerned with predicting $y$ given some values $X$ as in $P(y|X)$.