as I know, they both explain about how gravitation work.
But how they different? which one is the most correct?
Answers and Replies
All theories of quantum gravity are hypothetical, and unproven. So nobody knows if they are any more or less correct than Einsteins general relativity. Quantum gravity is different from classical gravity at extremely short distances/large densities, but experiments have not yet been able to probe such tiny distances.
Einsteins general relativity is the accepted model of gravity in current physics. The most common opinion is that it breaks down at the centre of black holes, since it predicts geometric singularities there.
In conclusion, the most common opinion among physicists today is that no phenomena have been experimentally observed that says anything about the validity of the different theories of quantum gravity.
No way to answer your question in a brief way. In general relativity means that of Einstein; there are a number of competing quantum gravity theories...usually relativity works well at large scales, like planets, galaxies, and the entire cosmos; quantum gravity is mostly small scale.....neither works at Planck scale...