You are asking the wrong question. More interestingly, consider this: Why types of errors do humans vs computers make for which kinds of tasks?

@cowlinator That's a bit like saying that $\pi$ is an algorithm because you can compute it to arbitrary precision with a suitable algorithm. 😉 But yes, you can simulate an NTM with a DTM in a certain sense. If you do it right, you'll find an answer of the NTM, if it does indeed compute any. However, most "metrics" you apply to NTMs will be skrewed. That all said, you seem to be focused on the first part of my answer; I suggest you read on below the line, which I think illustrates some inherent differences that may help.

I think the answer to this question is a textbook. For your own research, you may try and find out how tools like ElasticSearch work. Most likely, in practice, the correct answer is a combination of clever distributed algorithms/data structures, selectively applied AI/ML techniques, and raw processing power.