If you underestimate someone, they can do more than you believe they can. If you underestimate something, it is bigger than you thought it was. "I underestimated Mary. She is a great contributor to our team and I'm glad she was the person hired instead of the person I had recommended. "Many people underestimated the impacts of the snowstorm and now they are at home in the cold and in the dark wtihout enough food."
Originally Posted by Mr.Lucky_One
If you underappreciate something, you don't realize how good it is, how valuable. Susan felt underappreciated at work when her coworkers got a trip to Bermuda and she got a $50 gift card for the project they all worked on.
There are times, however, when "appreciate" is used to mean "estimated." "We didn't appreciate how much damage the CEO's affair would have on the company's reputation."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.