There really does need to be some descriptions here. The two sites seem so similar that I'm unsure which is the proper one to use for certain math issues. In what situations would you use MathOverflow over Mathematics Stack Exchange?
From the help centers of both sites:
MathOverflow's primary goal is for users to ask and answer research level(1) math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields
For more information see these posts,
Questions about problems in a mathematics course or textbook, and about understanding math concepts are appropriate.
Questions about software used by mathematicians are also on topic (with the exception of Mathematica because there is already a Stack Exchange site devoted to that, Mathematica SE). Questions about solving math puzzles are welcomed.
- Math Overflow's primary goal:
is for users to ask and answer mathematical questions related to current research in mathematics... [also] questions when reading scholarly journals or advanced graduate level books in mathematics.
MathOverflow is not for homework help.
If you aren't sure whether a question belongs on Math Stack Exchange or Math Overflow, or somewhere else on (or off) the Stack Exchange network, this Math Overflow meta answer should be helpful. It lists several related SE and non-SE Q&A websites.