Emotions are bodily reactions to a stimulus. Essentially emotions are physical and instinctive. They have been programmed into our genes over many, many years of evolution to be a survival mechanism. For example: You are on your own and on foot in the savanna wilderness, you see a lion, and you instantly get scared.

Emotions can be measured objectively by blood flow, brain activity, facial expressions and body stance.

Emotions are carried out by the limbic system, our emotional processing center. This means that they are illogical, irrational, and unreasonable because the limbic system is separate from the neocortex, the part of our brain that deals with conscious thoughts, reasoning and decision making.

Feelings on the other hand play out in our heads. They are mental associations and reactions to an emotion that are personal and acquired through experience. The emotion comes first and is universal. What kind of feeling(s) it will then become varies enormously from person to person and from situation to situation because feelings are shaped by individual temperament and experience. Two people can feel the same emotion but label it under different names. For example: You are in a zoo on your own and on foot, you see a lion behind bars, and your  feelings may range from curiosity to admiration or bitterness if you believe lions should never be caged.

(See the original text at http://www.laughteronlineuniversity.com/feelings-vs-emotions/)

 

Antonio Damasio, professor of neuroscience at The University of California and author of several books on the subject, explains it as:

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Feelings are mental experiences of body states, which arise as the brain interprets emotions, themselves physical states arising from the body’s responses to external stimuli. (The order of such events is: I am threatened, experience fear, and feel horror.)"

(Source: https://www.thebestbrainpossible.com/whats-the-difference-between-feelings-and-emotions/)

Damasio talks with The New York Times' David Brooks about emotions and the science of being human. He describes the difference between emotions and feelings, and explains why emotions are one of humanity's most important survival mechanisms: