When evaluating an interface these two terms are very important. How do they differ from each other ?
closed as too broad by Devin, Mayo, Graham Herrli, msp, JohnGB♦ Apr 22 '16 at 10:22
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Usability is the practice of taking human performance, human cognition, and collaborative group dynamics for maximizing the ease-of-use of a system. That system can be a human-computer, human-machine, human-human, or any additional combination of human(s)-thing(s).
The field has its origins in the 1960's and 1970's of Human Factors Engineering, and has evolved over the decades taking in ideas of Cognitive Science and Engineering as well as Organizational Task Analysis.
Jakob Nielsen has a nice short article on Usability 101: Introduction to Usability in which he defines 5 basic qualities.
Learnability: How easy is it for users to accomplish basic tasks the first time they encounter the design?
Efficiency: Once users have learned the design, how quickly can they perform tasks?
Memorability: When users return to the design after a period of not using it, how easily can they reestablish proficiency?
Errors: How many errors do users make, how severe are these errors, and how easily can they recover from the errors?
Satisfaction: How pleasant is it to use the design?
On reading the article you will notice that it is pretty computer centric and, given my definition of Usability above, you can create a "human-computer" relationship within usability.
Human Computer Interaction is the intersection of computer science and social, cognitive, and behavioral science. Taking what the field of usability has learned over the years and applying it directly to a human-computer system.
Ideas such as software engineering, software psychology, and computer graphics, all play a role in focusing the tools and techniques of usability to the interaction between the user and the computer software they are using.
Usability methods are HCI methods. There aren't many methods within usability that do not translate into HCI; they are simply focused on the specific interaction being looked at Though there are aspects of usability that might not apply to the more computer centric nature of HCI. In the same way, there aren't many HCI methods that would not considered aspects of the parent usability - they have just been made more specific to the human-computer relationship.
Simply put, HCI (Human Computer Interaction) is basically the way humans interact with a computer and usability is determined by how easily user is able to learn and accomplish a task while interacting with the computer via its UI. If the UI is not usable, the cognitive load on the user is high, the user might end up not using it at all.