The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree of two trees, is established by means of simple constructions, which allow one to obtain the largest common subtree from the smallest common supertree, and vice versa. These constructions are given for the problems of isomorphic, homeomorphic, topological, and minor embeddings. They can be implemented by a straightforward extension of any algorithm that solves one of the two problems, and the extension only takes time linear in the size of the trees.