What is the difference between applied mathematics and mathematics?

Someone may guess that applied mathematics and mathematics is same things. But in really applied mathematics have a so far difference from mathematics. Mathematics is a science of computation. On the otherhand applied mathematics focusses on the topics where mathematics have a wide range of use. Let classify mathematics in the following class, such as arithmatic, algebra, geometry, trigonometry, calculus: differential calculus or integral calculus. All above are the process of computation. Applied mathematics is focusses on physics, computer science, planetary motion, plasma science, etc. Economics is a part of applied mathematics. Not only that statistics, probability, heat and wave all are the application of mathematics. Whatever surrounding us everything we will find that each things are happening by a mathematical role.