If I make improvements to something, it usually means that I have completed whatever it was that I wanted to improve. If I make progress at something, it is positive, but it also implies that I am not finished with whatever is that I am trying to accomplish. I could say that I am making improvements to the house, building, repairing, etc. I could say that I am making progress in the improvements. It means that I have accomplished something, but I haven't finished the improvements.

"make improvements" is like updating a software, and it can better the quality of the subject. "make progress" probably means the same as "make improvements" in terms of quality, but it can also mean that something gets closer to its terminal or achievement regardless of quality or without the change of its quality.

Both are very similar "make improvements" [ make a bit of progress towards understanding something] and "make progress" [ to go forward in doing or understanding something. Example: The student needed to make some improvements in his oral English . After making improvements in his pronunciation, the student made progress in his oral English.