What is the difference between Quantum Mechanics and Quantum Field Theory?

An excellent explanation from Barak Shoshany
http://www.perimeterinstitute.ca/people/barak-shoshany

Quantum mechanics is just a set of mathematical tools, a framework, for formulating physical theories. It doesn't tell you anything about particles, or fields, or anything similar. It only tells you about quantum states, amplitudes and probabilities. See In layman's term, what is a quantum state?

Now, you can apply this framework to particles, or you can apply it to fields, or to a variety of other stuff. But every "quantized" theory, including quantum field theory, is built upon the basic principles of quantum mechanics - quantum states, amplitudes and probabilities.

In other words, think of quantum mechanics not as a physical theory by itself, but as a set of basic mathematical rules every self-respecting physical theory must obey.

By the way, quantum field theory itself is also nothing but a framework for formulating physical theories; for example, the standard model of particle physics is the most accurate theory we currently have of forces (except gravity) and matter, and it is formulated using the framework of quantum field theory.