In everyday use I think intuition is using your five senses combined with your experience to understand what you are are perceiving. The speed of recognition is unconcious so seems to come from nowhere. To recognise a correct pattern and an incorrect one.
Counter-intuitive means the solution is opposite to what you would imagine from common knowledge.
For example to lose weight eat more. More good food that is.
Instinct is inborn. Intuition is developed.
Intuition is an interesting subject. Check out Gary Kleins work some day.
Amazon.com Review
Gary Klein studies decision-making in the field, tagging along with firefighters, standing by in intensive-care units, and watching chess masters play lightning-fast "blitz" games to learn how people make choices with time constraints, limited information, and changing goals. From this research, he and his associates have developed a theory of "naturalistic decision-making."
Sources of Power essentially lends the validity of scientific research to techniques that many of us use every day. There's intuition, which is based not on instantaneous insight but on the rapid (perhaps even subconscious) interpretation of perceptual cues.