What is the difference between PDCA and PDSA?

The concept of PDCA is based on the scientific method. It was popularized by W. Edwards Deming. He later changed it to PDSA and called it Shewhart Cycle.

Both PDCA cycle (Plan, Do, Check, Act) and PDSA cycle (Plan, Do, Study, Act) are the iterative problem solving and continuous improvement approaches, where you make changes based on feedback from testing or observations of how things work. 

The idea behind PDCA or PDSA is that by making small adjustments over time, you can improve the process significantly.

 The only difference in these two approaches is the third stage: Check vs. Study

To Check or to Study?

Checking involves comparing the results to the expected results. The question here is "How do the results compare to what was expected?".

Study of the other hand is the deeper introspection of results. The question here is "What can we learn based on the results ?". This involves in depth analysis of results, rather than just comparing them with the expected results.