what is the difference between membrane potential and action potential?

The action potential is a special example of a membrane potential.  There is the resting membrane potential, where the cell is at rest, and the inside of the cell is negatively charged with respect to the outside of the cell. When the permeability of the membrane changes to certain ions (mainly Na and K), you get a depolarization, and the beginning of the action potential, if it is sufficient.  This depolarization travels down the axon until it reaches the nerve terminal where it depolarizes the membrane, and permits transmitter to be released as caclcium enters the cell.  The transmitter diffuses across the celft, and acts on the target neuron to either excite (depolarize) or inhibit (hyperpolarize) the cell.

The simple answer to the first question is: an action potential is a changing potential - thus the term "action".  

So the membrane potential remains steady until something happens to cause it to change quickly.  That changing potential happens at one spot on the membrane,  but it causes the same thing to happen at another spot, which causes it to happen at another spot, and so on.

In other words, once an action potential happens, it generates another action potential and then another - along the membrane.  That progression of action potentials is the nerve impulse.