Sensibility

Sensibility refers to an acute insight of or responsiveness toward something, such as the emotions of another. This theory emerged in 18th century Britain, and was closely related with studies of sense perception as the means through which knowledge is collected. It also became associated with sentimental moral philosophy. 

Sensibility is your sensitivity to stimulus or other things that make you react in a certain way. It can be described in many ways such as: 1) The capacity to respond to an emotional situation with a refined feeling. 2) The ability to receive sensory input. 3) Having reason and sound judgment. 4) Feeling or perceiving a thing to be real.

Sense

A sense is to a living being as an input device is to computer. Senses are physiological abilities of organisms that give data for perception. The senses and their classification, operation and theory are overlapping topics studies by a range of fields, particularly neuroscience, cognitive psychology, and philosophy of perception. The nervous system has a precise sensory system or organ, dedicated to each sense. 

Members of the animal kingdom, including humans, have five major senses, sight, hearing, smell taste and touch. Some species have unique senses, like the birds have the ability to navigate by sensing the earth’s magnetic field. Moreover, many humans and animals have shown the capacity to sense things without sensing to sense things without using the know senses. Examples include dogs who know when their owner is hurt, animals who try to run away just before an earthquake, and humans who are remote viewers, psychic mediums, etc.