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Differences between mathoverflow and math.stackexchange.

Recently I read on mathoverflow the comment that the question better to ask on math.stackexhange. If there is any striking difference between these two sites which one should know before asking his question?

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    $\begingroup$ MSE welcomes math questions at all levels, but MO does not generally welcome questions lower than research level. $\endgroup$ – Bill Dubuque Jul 19 '11 at 22:00
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    $\begingroup$ @Bill: I'm really interested in how do people define "research level". Is it different from "research-related"? As my experience, sometimes people may need to ask some basic level question when doing research. $\endgroup$ – Jack Aug 4 '11 at 4:10
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    $\begingroup$ @Jack In practice it seems to mean graduate level or above - thought there are exceptions. $\endgroup$ – Bill Dubuque Aug 4 '11 at 4:22
  • $\begingroup$ For my comment that follows, I need to define what I call a “dog-to-cat” error. Such an error is one where the erroneous expression turns out to be itself a valid expression. Such a mistake, such as misspelling “dog” as “cat” are hard to catch. (A. Do you see anything wrong with “cat”? B. No. A. But he was trying to spell “dog”!) Some jokes, of course, are based on this phenomenon. $\endgroup$ – Mike Jones Sep 28 '11 at 9:32
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    $\begingroup$ Could some users of this site who are not native speakers of English please comment on the question of to what extent English mistakes, especially what I call dog-to-cat errors (defined in my previous comment) impact their participation on this site? Bill Dubuque above used “thought” for “though”, which is a common slip of the pen even for native speakers of English (myself, and ESL teacher, included!). In this case, it amusingly results in another expression that is equally valid (and, by luck, roughly synonymous with the obviously intended text). $\endgroup$ – Mike Jones Sep 28 '11 at 9:33
  • $\begingroup$ This might be useful, as a supplement to the answer provided by @Asaf Karagila meta.math.stackexchange.com/questions/41/… That question had several answers and a lot of community participation. $\endgroup$ – Ellie Kesselman Nov 5 '11 at 21:43
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It is the level of the questions.

My rule of thumb is that if the question could be answered during an undergrad/basic grad level course material then it fits on MSE better.

If the question rose from a rather advanced topic or a research related question, I will post it on MO.

My personal exception is advanced questions in descriptive set theory, since MO harbors a larger crowd of mathematician with extensive knowledge in this field (in comparison to MSE)

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