Basic Trope: The white guy is better at native stuff than the natives are.
Straight: A white guy, coming from a city, becomes better at fishing with a spear within a week, than a Native American, who has been fishing with a spear his entire life.
Exaggerated: A white guy, coming from a city, manages to become better at fishing with a spear, shooting with a bow, riding a horse, wrestling bears, etc, than any other member of the native tribe, and is quickly appointed chief. All within a few days.
Downplayed: Despite living his entire life in the city, it turns out the white guy is pretty good at spear fishing. For a white guy. He's better than the other white guy anyway. Compared to a native, its not impressive.
The white guy has access to better health care, nutrition, education and technology. A lack of familiarity with an activity is only a minor disadvantage for him, one he easily overcomes. Also the native is likely an inbred hick from a small, poor, isolate, unimportant village largely forgotten by time where parasites, starvation, chronic sickness, poverty, ignorance and worse problems plauge everyone.
The Native American was the village idiot, and the white guy had spear fishing as one of his hobbies.
The white guy is conscious of the fact that he is at a disadvantage and works crazy hard to learn, while the non-white rival is complacent in his skills.
The white character is doing things better than the non-white, but it's always things that learning from an advanced society would help with, such as building or creating traps. The chief is taking advantage of the advanced knowledge that the white has to help them, which is why he seems to be doing better.
Inverted: A Native American goes to a city and becomes a better pilot/programmer/rock musician than anyone else.
The white guy looks like he has mastered the technique but he never manages to outdo the Native American.
It turns out that, in fact, both are Native Americans or both are white — it's just that only one looks it.
The white guy does better with spear-fishing but never catches up to the Native American in anything else.
Double Subverted: The white guy, realizing that his technique is flawed, uses some of his "street smarts" and ends up blasting the Native American out the water.
Parodied: The white guy's successes are all down to luck—in reality he's a bumbling fool...and as soon as he tries to use his skills against a really dangerous opponent, the natives have to rescue him.
Zig Zagged: The white guy looks like he's mastered the art of spear-fishing... but the natives are still better... so the white guy draws on his unique experiences and does become better than everyone else... but he still fails miserably at everything else the non-white characters consider normal... but the skills he has and they don't eventually win him some respect... as the local Bunny-Ears Lawyer.
The white guy is not especially better at anything than the Native American.
There are no white characters or no non-white characters in the cast.