The question posed was "how do they differ?" not "how important is that difference?". If you ask me the latter, I'd say that for many domains it's not that important (see the caveat below.) On the other hand, for Google and Facebook and similar companies it's certainly very important, which is why all their interviews are mainly about how well you can reason about algorithms and data structures.
Caveat: These problems might not happen often in less data intensive domains but, when they do happen, they are certainly very important in my experience.
> The question posed was "how do they differ?" not "how important is that difference?"
And the question arose from the claim that the formally taught and self-taught programmers take different approaches in general. It goes without saying that a problem that can be solved effectively using a trie will be approached in 2 different ways by someone who knows tries and someone who does not. The claim made in the OP was broad, and I am saying about 80% of the time, an auto-didact and a CS person will solve it the same way. Claiming that because sometimes a CS person can use insights which the non-cs guy doesn't have doesn't equate to different approaches.
The fact that 80% of the time the approach is not important to get the desired result because the task only operates over small n or similar does not mean that the approaches are equal.
Caveat: These problems might not happen often in less data intensive domains but, when they do happen, they are certainly very important in my experience.