I don't if she is so much intelligently gifted as just extremely motivated and curious. Is there even a difference?
There can be a big difference, but there's no magical binary distribution between the two. Some kids are both, some are only one or the other. Lots blend in the middle. Really bright, motivated kids tend to be really good at doing the normal stuff of school and life. They are well positioned for success in whatever they set out to do. Really gifted kids tend to be divergent thinkers, which can sometimes make them really bad at doing the normal stuff of life.
But there's also no clear line between "gifted" and "not gifted", just tendencies that seem to increase the farther you get from the norm. From what I can see, the further you move away from typical and towards HG or PG, the more likely you are to see those greater extremes of divergent thinking - and, often, the lousier the kid will do in a regular classroom.
A favorite quote of mine, somewhat paraphrased for thinking about what differentiates gifted vs bright/ high achieving, is "Talent hits a target no one else can hit. Gifted hits a target no one else can see."
Teachers do not like children who are aiming at targets they cannot see.
