What is the difference between project Crashing and Project Fast Tracking?

Both are Techniques used when the project schedule needs to be shortened (schedule compression) either because of any risk that occurred or management’s decision. Crashing a project is done by getting more resources to work on specific project activities to make its duration lesser.  Whereas Fast Tracking a project is to change the dependencies among sequential activities and run them in parallel.

Crashing and Fast Tracking are schedule compression techniques. You apply them in order to shorten your schedule and to reach a certain schedule target.

Fast tracking means executing two activities at the same time, even if they would normally not be done in this way. Fast tracking is free but adds additional risk to your project.

Crashing means to add additional resources to your project. Crashing requires additional budget. So you want to crash those activities that give you the biggest bang for the buck  -the most schedule compression at the least cost.

Both techniques only make sense if you apply them to activities on your critical path so all depends of situation in project.  

One of the goals of crashing the schedule is to minimize the incremental cost. However, in exchange for completing some work ahead of schedule, crashing usually always leads to some additional incremental cost to the project. If you're willing and able to spend more to accelerate the schedule, fast-tracking may be a viable option for you.