The ID3 algorithm generates a decision tree from a dataset using a recursive approach, splitting data into child nodes based on attribute values. The algorithm creates a decision tree that can be used to classify new test cases by working down the tree. On the other hand, the Apriori algorithm is a influential concept in data mining, generating frequent item sets and individual frequent item sets. It uses pseudo code to increment candidate item sets and find the minimum support value, returning the final frequency value.