A decision tree and a random forest are both machine learning algorithms used for classification and regression problems. However, there are several key differences between the two.

A decision tree is a type of model that makes predictions by recursively partitioning the input space into smaller and smaller regions, known as branches or leaves. At each node in the tree, a decision is made based on the value of a feature that maximizes the separation of the target variable. The final prediction is made by following the path from the root of the tree to a leaf node. Decision trees are simple to understand and interpret, but they are prone to overfitting and can easily capture noise in the data.

A random forest, on the other hand, is an ensemble method that builds multiple decision trees and aggregates their predictions to make a final prediction. In a random forest, each tree is built using a random subset of the features, and the final prediction is made by averaging the predictions of all the trees. This randomization helps to reduce the variance of the model and prevent overfitting. The resulting model is more robust and can produce better predictions on unseen data.