One handy definition of intellectuals is that people who expect their opinions taken seriously in field X based on prestige built in an unrelated field Y. A classic example is Einstein writing about socialism based on the prestige he acquired in physics. More general example is writers, people-of-letters, literature and poetry folks engaging in politics. If we would accept it, Hayek and Sowell were not intellectuals, they never wandered too far from the field they actually had expertise in.

But why accept such a quirky definition? They logic behind is: when you are, say, an economist, and pontificate about economics, you are acting actually as an economist. When you are a physicist or writer and pontificate about politics or economics, you are obviously not acting as a writer or physicist but as a Generic Smart Person. Being a good writer or physicist proves you are smart (roughly: true enough), and you expect people to accept your opinion because you are smart. The unspoken assumption is that smartness matters more than expertise in forming correct opinions. Thus people who expect people to accept their opinions about economics because of their expertise are called economists, and people who expect people who accept their opinions about economics (or anything) because they are smart are called intellectuals: people whose defining (social) feature is the intellect, not the expertise.

On a more broader view, ideally, people should expect their opinions to be accepted because they are actually well evidenced and argued, not based on authority. But the "masses" tend to accept views based on authority. So the expert uses the authority of expertise and the intellectual uses the authority of generic smartness (which is proven by success in an unrelated field.)