Telepathy is the paranormal ability to directly contact the mind of another living being. This may include both "hearing" the thoughts of other people as well as "sending" thoughts into the minds of others. Especially powerful telepaths may be able to control the actions of others with their ability. Telepathic ability is a common feature of science fiction stories.
Empathy is a limited form of telepathy sometimes found in science fiction. Generally, empaths are able to perceive a person's emotional state directly, but they are not able to discern actual thoughts.
Telepathy in Star Trek
Telepathy is typically a racial attribute in Star Trek. Races known for telepathic ability include the Vulcans and Betazoids. In early depictions involving Vulcans, telepathy was a very limited ability requiring discipline to learn and intense concentration to achieve. The TNG-era introduces the Betazoids, who are able to send and receive detailed thoughts with little or no effort.
Resistance to telepathic ability is also a racial attribute: the Ferengi, for instance, are resistant to Betazoid telepathy.
Telepathy in Star Wars
In Star Wars, telepathy is one of the paranormal abilities associated with the Force. Jedi and Sith have shown that they can send thoughts to other people (especially those with Force affinity) or pick up surface thoughts from others, but Force-related telepathy is usually rather limited in scope. They can also influence the behavior of people who are "weak-minded", although the meaning of that description is unclear.
Telepathy in Other Science Fiction
In Babylon 5, telepathy is a genetic trait introduced to the Young Races by the Vorlons, who kidnapped individuals of various races, genetically modified them to carry genes for telepathic ability, then returned them to their homeworlds to spread the new genes. Telepaths vary in ability, and some races instituted breeding programs to produce the most powerful telepaths possible. The effect of the emergence of telepathic ability upon society was a recurring theme of the show.