I was thinking the other day about how many different types of knowledge there were.
1. Common Sense. This is knowledge gained from experience, observation, or instinct. "Don't touch hot things" and "don't insult someone bigger than you" are prime examples. This isn't things you necessarily need to be taught, and they don't teach it in school.
2. Book learning. This is knowledge learned in school. 2+2=4, Ethiopia is an African country. Knowledge that may or may not do you good. Basically, knowledge that helps you score high on standardized tests and get into college.
3. Wisdom, or application of knowledge. This is separate from common sense because people with common sense may not always have wisdom. This is "smarts" that aid you in discernment and in difficult choices.
4. Observation. This aspect of smartness can be hard to teach. This is body language, tonal reasponse etc. that helps you determine or know more about people or things without being told.
I don't know if these are all the forms, but 4 was all I could come up with.