Claircognizance is the idea that people can receive thoughts, words, and ideas transferred to them from the non-physical entities. 

Typically considered one of the sixth senses and generally reserved for those who are more mental in their thoughts and ideas, most people believe that a claircognizance is a mental-based form of communication that occurs between the receiver and disincarnate beings such as spirit guides, angels, aliens, and/or the deceased.

Spirit channelers, such as Ester Hicks, are thought to receive their information through gifts such as claircognizance. 

Claircognizance is different from clairaudience, where clairaudience allows the receiver to hear and distinguish single words, and claircognizants often receive entire ideas or concepts in what some refer to as "a mental download" of information. 

Claircognizance is a common gift among:

• Inventors
• Mathematicians
• Musicians
• Engineers
• and others in STEM professional fields

The concept of claircognizance is considered to be so similar to the idea of radio transmission, that around the time of the 1920's when the invention of the radio came about, making it so thoughts and ideas traveled through space and time with no physical connection, Thomas Edison, saw the link.

The famous American inventor then planned to create a device to capture spirit voices people were already hearing, and though no device was ever found, thanks to his early forays in the idea, there are plenty of such sound capturing devices now available on the market. Here are some available from GhostShop and here's some from Digital Dowsing. While you can purchase hobby level equipment to capture what one can also receive in their mind, keep in mind the more expensive your equipment generally the more sensitive the meter, and the more accurate and reliable the reading. 

How is telepathy related to claircognizance? 

Telepathy is officially defined as: 

From the Greek τῆλε, meaning "distant" and πάθος, pathos or -patheia meaning "feeling, perception, passion, affliction, experience" is the purported transmission of information from one person to another without using any of our known sensory channels or physical interaction. 

- Wikipedia (source)

And in short:

Telepathy is basically the same concept as claircognizance though rather than referring to someone receiving thoughts, mental communication and mind connection from disincarnate non-physical beings, the person who is telepathic receives the thoughts from someone living, usually another person or animal. So, the difference is in relation to who the perceived sender of the thought or idea is. 

Claircognizant receptions are thought to be those received from non-physical sources, telepathic receptions are thought to be received from living (human, animal or plant, or any being considered capable of conscious thought) sources. 

All in all, generally, someone who is claircognizant is also telepathic and vice versa. Both refer to the same mechanism of reception, transferred mental thought, however, the difference in name comes from where or who the thought or idea received, is considered to be received from. 

PS: It is widely believed that both claircognizance and telepathy (referring to thoughts received psychically), and clairvoyance and remote viewing (referring to images received psychically), all defy the general laws of classical physics, thus, making the laws of physics incomplete. This is not too big a deal, though, as many, if not most scientific laws are considered incomplete.