Question

what is different between self-inductance and mutual inductance?

Answer 1

imagine a coil, and a current passes through this coil. Magnetic field in that coil created by the passing current (actually the CHANGE of current, but don't worry about that now) will induce the potential difference on the coil BUT in the opposite direction of the potential difference that the first current made.
That is self-inductance, the coil induces voltage on itself with the magnetic field created by the change of current that passes through it.

Now imagine you can create a magnetic field with one coil and somehow transfer that magnetic field to some other coil (and you CAN do that, it is the basic principle of transformers). The second coil would, under the effect of magnetic field induce voltage. That is called mutual inductance, creating a magnetic field in one coil and using the same magnetic field to induce voltage on the other coil.

If you need some equations or something just ask and I'll try and help.