The terms are not completely synonymous, but I would argue a person who has no interest in either formal or informal education is not and will never be intelligent. After all, a person who refuses to educate him or herself despite knowing he or she possesses the capacity to understand such information is a person who willingly keeps him or herself in a state of ignorance. Those who are willfully ignorant have decided that ignorance is more valuable than knowledge. Those who make that decision are unintelligent--and, not only unintelligent, but dangerous to society, particularly societies founded on principles of democracy.
Studies show IQs are highly malleable figures that can be increased through practice. Similarly, the ability to think critically and logically can be dramatically improved through practice. Educational institutions provide environments where such skills can be practiced regularly; and, in fact, schools often demand their students to practice such skills daily. Though it is not necessary to reap these benefits by studying at formal institutions of higher education, it would be ridiculous to believe individuals who do not pursue the development of such skills at even informal capacities are generally as intelligent as people who regularly seek to develop these skills at informal or formal capacities. Studies also suggest that intelligence can decrease over time if no activities are taken to maintain it.
In other words, a person cannot expect to sit on his or her ass all day and still expect to be called intelligent. While you don't have to attend college, you do have engage in some activities in order to utilize and develop intelligence. A child who scores in the above average category at 8 but decides to never touch a book or attend a lecture or even enroll in school again will not be as intelligent as a child who has diligently developed his or her average intelligence when they both run into each other again at age 30.
I also think it would be ridiculous of me to argue that education has had no impact on my overall intelligence. While I have scored very high in intelligence tests since childhood, I believe education has had a consistently beneficial effect on my intelligence. My ability to comprehend texts and analyze arguments is much greater today than it was 7 years ago, before I had attended college or law school. My intellectual abilities and skills have increased as I have continued to participate in activities that have encouraged the development of my intellect. While I do not think formal education is necessary for such development, I must argue that education of some sort--formal or informal--is necessary for the development of intelligence. You don't have to go to college or grad school, but you do have to do something that exercises and challenges your mind in order to become or remain highly intelligent.
I would also point out it is not necessary for a person to endure several years of schooling in order to be highly educated. Autodidacts are often highly educated--and yet, they often do not possess formal recognitions of their education. Leonardo da Vinci was an impressive autodidact, for example, and I think the phrases 'highly educated' and 'highly intelligent' would apply to him in equal amounts. However, I would also argue he was so highly intelligent because of his desire and ability to self-educate. Similarly, writers like Borges, Hemingway, and Lovecraft were autodidacts, and I would argue they would not have been such intelligent authors if they had not educated themselves at all. In short, I think it is impossible for intelligence to exist outside of education--but I do not think education exists solely within the confines of schoolyards.
