Real giftedness often reveals itself in a different way of thinking. Yes, most "gifted" kids are also bright; school is easy for them. But they often arrive at the correct answer by rapid following of long, meandering paths that would never have occurred to their plodding teachers. Gifted kids arrive at incorrect answers in similar ways. They mispronounce big words because they meet them in print before they hear them spoken. They are bothered by coincidence and endeavor to connect things with separate histories. And so on.
An example from my own youth. When I was a mere boy*, there was a cartoon on TV featuring King Leonardo, a lion ruling over Bongo Congo. His true-blue prime minister -- who was much smarter than the king -- was a skunk named Odie Colonie. "Odie Colonie" is a joke, a pun, of course. But in considering why the joke was funny, I originally thought that it was a reference to Odo Colonna -- a name I vaguely recognized from reading history books (who later became Pope Martin V). It took me a while longer to make the connection with eau de cologne and the skunk's scent, and even when I realized that was probably what the producers had it mind, I preferred my original supposition.
When I was doing a practicum in teaching with eighth graders, I gave an extra-credit assignment. I said, assume that George Washington was captured after the Battle of Monmouth. Write the subsequent history of America from that point. Only two kids dared the assignment. One was a dull but earnest effort from one of the kids with good grades who just couldn't pass up a chance to rack up some more points. The other was by a boy who probably had ADHD (not properly diagnosed at that time), and who was barely scraping by with Cs and Ds.
The scraping-by boy's essay had Washington transported in chains to Britain and the Revolution quashed, whereupon it turned into a smoldering insurrection not unlike the Troubles in Northern Ireland. The low-grade terrorism and guerilla warfare finally ended when the Martians landed and enslaved everybody. Unlike his earnest but dull counterpart, this kid could imagine the consequences which flow from actions. Fanciful though his alternate history turned out, his was the better understanding, and the more obviously "gifted" approach.
*King Leonardo and his Short Subjects premiered in 1960 and ran until 1963 on Saturday morning cartoons. It then went into syndication, I think. How I recognized the name "Odo Colonna" sometime between the ages of seven and ten boggles my mind even yet, but I did. Many gifted kids have minds stuffed as indiscriminately with bright little facts as a jackdaw's nest.