What is the difference between neurons (nerve cells) and nerves?

A neuron is an individual cell of the nervous system. Neurons communicate with one another and other tissues through long processes that extend from their cell bodies.
Fibers of multiple neurons serving a similar function can come together and be wrapped up in a piece of connective tissue. These fibers and their surrounding connective tissue together is called a nerve.
Simply,
A neuron is an electrically excitable cell that processes and transmits information through electrical and chemical signals.
A nerve is an enclosed, cable-like bundle of axons (the long, slender projections of neurons) in the peripheral nervous system.
Neurons are found in the brain, spinal cord and peripheral nerves.