The main difference between Gibbs, EM, and the Greedy algorithm lies in their maximization step after computing their Z matrix. Examples of the Z matrix are graphically represented below.THis Z matrix is then used to recompute the original profile matrix until convergence. Some examples of this matrix are graphically represented by 17.8
Intuitively, the greedy algorithm will always pick the most probable location for the motif. The EM algorithm will take an average of all values while Gibbs Sampling will actually use the probability distribution given by Z to sample a motif in a step.