They are very close, but they are different.
I can understand something without using any more than the simplest thought processes. Also 'understand' is used in a general case.
I understand English without trying.
I understand hunger because I have been hungry. I didn't have to use logic to solve a problem.
In the general case, I understand mathematics (at least some) because I studied it in college.
If I figure out something, the answer was not necessarily obvious. I had to apply some thought and perhaps logic to have an understanding.
I figure out a math problem.
I figure out that there is a fire nearby if I smell smoke.