You described your friend's childhood drawings as "a little less "hurried", as she obviously loved doing it and spent more time on a drawing", and I think this is the key. She liked drawing as a kid, which made her draw more than her peers, she got better at it and because people generally like doing things the more the better they're at them, a positive feedback loop started.
It also suggests a practical approach to get good at something: sit down, practice, and ignore the discomfort you'll be feeling at the beginning. Many people considered talented simply didn't have that initial discomfort, so they drifted into a skill early, whereas for non-talented it is a barrier to entry.
I have another acquaintance who's a musician (an actual musician, unlike me -- I'm just a programmer who likes playing the drums). The guy obviously had a lot of practice, especially as he graduated a famous music academy so he had to play the violin a lot.
That being said, he started taking violin lessons when he was 6, but by that time he could play it pretty well. Having realized that he can't remember the songs he was inventing, he even developed his own rudimentary notation system (when he was about four), with horizontal lines whose length indicated direction and a combination of dots and relative heights to indicate pitch relative to the first note of the song, so that he only had to remember where to start from. His violin technique was also remarkably good. When he started giving violin lessons himself, he struggled with understanding the first gripes of beginners a lot more than he'd expected. For instance, he never realized it takes so long to learn how to properly angle the bow when playing the second and third string of the violin (they're at almost equal height with respect to the base of the resonance box, so most beginners will unintentionally stroke both at the same time). Not only did he not remember having that problem, he literally never really imagined that someone could have that problem.
He's one of those people who does have an innate talent; there are a lot of techniques that he never learned, nor really "discovered" through an iterative process, he just figured out it would sound good if he did <something>, and it did. His brain was wired in a manner that's favourable to playing the violin and to music in general.
Needless to say, he still had to practice a lot -- he had to learn "proper" notation, he's constantly refining his rhythm and coordination, he had to learn how to play in an orchestra, and it's not like he could play any piece, no matter how difficult, from the very beginning. But there were things which his mind and his body could do without being taught, or which, at least, they discovered a lot more quickly than others did. They weren't enough to make him an orchestra-level musician from the moment he set his tiny three year-old hand on a violin, but they are certainly enough to set him apart from a lot of musicians of his age and experience.
Among the artists I know, some have taught drawing at art schools. They've all said drawing and art talent are altogether separate matters. Drawing is about reproducing measurements, a skill anyone able to hold a pencil can learn. Geometry class might be a good start.
> ... the ones whojust practiced a lot. have a talent for this are the likes of Picasso ... Everyone else ... just practiced a lot.
Actually even the geniuses had to practice. For example, Van Gogh started painting when he was ~23, and the first couple of years he was quite bad at drawing. With practice he improved, and went on to produce 900 paintings in his short lifetime. Manet, the first French impressionist, was so bad starting off he had to cut out the good portions of paintings and sell those separately.
Your a. and b. programmers aren't really distinct, many of the geniuses of the field speak about dismal "failures" from which they learned. It probably requires genius to see the truly important mistakes and how to do things better.