A hurricane is a tropical cyclone that forms in the equatorial (tropical) region of the Atlantic ocean, usually off the coast of Africa. During the hottest parts of the year, warm and moist air from the surface of the ocean rises into the air and then condenses heavy rainfall with the relatively cooler air falling back down to the ocean surface. When allowed to organize, the central eyewall forms the core of the storm and the precipitation falls in bands that rotate counterclockwise in the northern hemisphere due to the rotation of the planet. The fuel source for hurricanes is warm, moist ocean water underneath them. As soon as they come over land, they begin to lose strength almost immediately.
Thunderstorms, on the other hand, generally form over land at a frontal boundary. The same basic mechanism of warm, moist air rapidly rising and then cooling and falling causes them to form, but they generally do not get large enough to allow for a larger, cyclonic effect to begin to form. Really potent thunderstorms called supercells can develop a cyclonic effect which can lead to heavy tornadic activity. But thunderstorms over land do not necessarily have to produce rain as a result. The energy in the system can be dissipated just through the cloud to ground lightning with no associated precipitation if the air is not too moist.