While I'm simulating grover's algorithm, I found that with BasicAer backend it works well but with Aer it is not. What is the difference between
Regarding to the difference between BasicAer and Aer, take a look at this answer: https://quantumcomputing.stackexchange.com/a/4996/9858
And in term of BasicAer returns incorrect result, take a look here: https://github.com/Qiskit/qiskit-terra/issues/1838
Hope this helps.