Strangely, there is no quantitative difference in strength, speed, or damage caused by a cyclone versus a typhoon. The only difference between these two names for cyclical tropical storms are the global area in which they form. People around the Indian Ocean and Southwestern Pacific Ocean (that part of the Pacific Ocean near Australia) refer to these storms as cyclones and those storms that generate in the Northwestern Pacific Ocean (that part of the Pacific Ocean near Asia) are called typhoons. Incidentally, people around the Atlantic Ocean and Eastern Pacific Ocean (that part of the Pacific Ocean near the Americas) call such powerful, cylindrical storms hurricanes.
A low-pressure system that develops over the ocean during the right conditions might create thunderstorms and high winds that qualify it as a tropical depression. This storm could keep gaining energy from warm ocean waters and advance to a tropical storm if it has winds of 39-73 mph (62-117 km/hr). Once the rotating, centrifugal force exceeds these wind speeds, meteorologists classify it as a more severe tropical storm whose name varies based on its location.
If a severe storm churns somewhere in parts of the Northwestern Pacific Ocean (which is in the Eastern Hemisphere), we call it a typhoon. However, if this same exact storm were hypothetically dropped into the Indian Ocean or the middle of the Southwestern Pacific Ocean (which is still in the Eastern Hemisphere), we'd refer to it as a cyclone. Among cyclones, there are different names based on their locations. Severe cyclonic storm, severe tropical cyclone, and tropical cyclone are all variations of the same type of storm.
Even though some international meteorologists have universalized a cyclone to mean any circular wind system, for the most part its geographic specificity endures. One way to get a grasp on this distinction is by starting off with a flat representation of the world in its most common form (i.e., with the Americas on the far left and Australia on the far right). The left half of the map uses the term hurricane, the top half of the right side of the map uses the term typhoon and the bottom half of the right side of the map uses the term cyclone.
Another, more precise way to look at it is by considering meridians and other longitudinal lines. Storms in the Northwestern Pacific Ocean, west of the International Dateline or IDL (that cuts roughly between the Americas and Asia, located at 180° longitude) are called typhoons. Storms in the Indian Ocean or in the Southwest Pacific Ocean west of 160°E longitude (160°E longitude is just a little west of the IDL) are called cyclones.
In the northern hemisphere, storms turn counterclockwise, while in the southern hemisphere they rotate clockwise. One difference between a certain cyclone and typhoon might be their rotational direction. Most serious storms are created near the equator because of the ocean's temperature and currents, but sometimes they'll stray further away. Damage from these storms usually results when they drift over populated coastal land. They are separate phenomena from a monsoon, tornado, or tidal wave.