Both approaches use word lattices to represent and induce paraphrases since a lattice can efficiently and compactly encode n-gram similarities (sets of shared overlapping word sequences) between a large number of sentences.
the two approaches are also different in that Pang, Knight, and Marcu use the parse trees of all sentences in a cluster to compute the alignment (and build the lattice), whereas Barzilay and Lee use only surface level information.