The Photon answered this question excellently, but I feel there is some relevant information that should be shared and will be of interest to some readers or the asker himself.
Firstly, I will add that inductors can also store capacitive charge. This is a know phenomenon that can be made to manifest strongly by winding a bifilar coil and wiring the END of wire A to the START of wire B (SERIES wiring). By wiring them in series, you are effectively making one enormously long piece of wire in which each wire is adjacent to another turn whose voltage is 50% difference of the total voltage across the inductor. This was explained clearly in Nikola Tesla's patent "Coil for Electromagnets". His patent drawing shows a pancake coil but the effect works on ALL coils. By arranging wires next to each other, you can magnify the electrostatic field between the wires. And yes, if you do the experiment right, you can charge the inductor and cause it to store energy and then discharge the energy later. But even in an ordinary straight-wound coil, the charge and capacitive field is still there -- it's just so ridiculously small that it is generally ignored. However, it becomes apparent at high frequencies if you measure the Q of a coil. Spacing out turns in a radio coil increases Q because it reduces the capacitive field strength between windings.
Moreover, there is a noteworthy difference between inductor magnetic field and capacitive charge that makes them more different than most people think, and they really shouldn't be directly compared. Read on...
If you attempt to discharge a capacitor charged with 12 volts into another capacitor charged with 12 volts, nothing will happen because the energies cancel out. On the other hand, if you attempt to discharge an inductor charged with current coming from a 12 volt source into a 12 volt capacitor, the inductor will in fact supercharge the target capacitor to some level above its initial 12 volts. How high it goes will depend directly on the magnetic flux in the inductor and the capacity of the capacitor. If the capacity is very small, the voltage can be driven extremely high depending on other circuit conditions. To experiment with basics of this behavior, you simply need a diode and a little cleverness to charge the capacitor from the coil without letting it immediately discharge back the other way.
In fact, this very phenomenon is the whole reasons tank circuits are able to function at all. If the inductor didn't have the ability to overcharge it's target, tank circuits would never work. In a tank circuit, a capacitor fully discharges across an inductor until it reaches a voltage of essentially 0. If it weren't for the charged inductor, all movement in the circuit would stop at this point. But instead the inductor's magnetic field now acts as a charge pump and forces the capacitor into the negative region well past zero. After the inductor finishes discharging, the whole process reverses. You can do other more interesting things with this behavior besides primitive tank circuits.