A tropical storm is similar to a hurricane, except it's weaker. Tropical storms only have sustained winds of between 39 and 73 miles per hour. Tropical storms often become hurricanes. Furthermore, a hurricane can't become a hurricane without first being a tropical storm. Once a hurricane's winds drop below 74 mph, it has once again become a tropical storm.
You can think of a tropical storm as a step in the development of a hurricane. It has the same dynamics and structure (although no eye). It's just not as powerful.