A difference between the Program Evaluation and Review Technique (PERT) and critical path method (CPM) is that:

The difference is the Time Estimates

Explanation:

In the critical path method (CPM) the time estimated for all the activities in the project are assumed to be deterministic, while in Program Evaluation and Review Technique (PERT) the time estimate is assumed to be probabilistic.

When the major concern in a project is the monitoring and scheduling, the PERT techniques is used, on the other hand if the emphasis is on the optimization of resource allocation the CPM is used.

I must also add that these days both techniques are employed in the network analysis for project management

you need to be a high enough rank