Gaussian Process (GP)	Dirichlet Process (DP)
Primary Use Case	Continuous function approximation, regression, and uncertainty quantification.	Clustering, density estimation, and mixture models with an infinite number of components.
Mathematical Object	Infinite-dimensional generalization of a multivariate normal distribution.	Infinite-dimensional generalization of the Dirichlet distribution.
Output	A continuous function f(x) (with confidence intervals) mapping inputs to outputs.	A discrete probability measure (a set of clusters and their weights).