What are the key differences between the critical path and critical chain methodologies in project management, and how do these differences impact project scheduling and resource management?

The key difference between critical path and critical chain methodologies in project management lies in how they handle uncertainty and resource allocation. Critical path focuses on sequencing tasks based on their dependencies and estimates, while critical chain incorporates buffers to account for uncertainties and resource constraints. This impacts project scheduling by allowing critical chain to be more flexible and adaptive to changes, leading to better resource management and potentially shorter project durations.