CPM and PERT are both scheduling methods that use a common approach to design networks and determine critical paths. PERT focuses on time estimation with uncertainty, using three time estimates per activity, while CPM uses a single estimate and prioritizes time-cost tradeoffs. The key differences between CPM and PERT are that PERT is probabilistic and event-oriented, allows for uncertain durations, and does not allow crashing, while CPM is deterministic, activity-oriented, has known durations, and allows crashing to reduce time.