I don't use iOS (nor any other app store for that matter), but one thing that stands out in that screenshot is the lack of any description of what those apps actually do; the clearest one there is "Get Followers on Twitter", and that's just because it's the name of the app. It's not like there's no room to add a short one-line description either. (The images also don't help much because while they mostly show what the app looks like, that's still quite different than saying what it does.)
You are supposed to search for Twitter as a test. Tweetbot doesn't make much sense as a search term, at least for finding other Twitter clients. I think the search results are actually quite great, considering. (The calculator is an app by the makers of Tweetbot. I actually had that same use case before: I knew that some developer of some app made some other great app, but I didn't know its name – so I would search for the app I knew, go to it and then the dev’s page and then to the app I actually want. So showing other apps of that same dev in a targeted search for the most popular by far app from that dev makes total sense to me.)
I would argue the calculator is still a fail. If I searched or Tweetbot, the top hit should obviously be Tweetbot, but I would argue that the other results should be other Twitter clients. A calculator simply isn't. Even worse, the 3rd result is for a different tapped named "Tweetbot" When you scan through the results, Calcbot is really the odd one out. Now, if I had searched for Tapbot (the maker of Tweetbot), then sure, Calcbot makes sense.
Running a search for "tapbots" indeed gives me Tweetbot and Calcbot in the 1 and 2 slots, but the rest of the results are shit. Some competing apps, and of course "Resturant Fan Logo Quiz" in slot 4 for some reason. (It's in slot 5 for "tweetbot".)
These results are still, not very good beyond position 1. Perhaps Apple should simply start thresholding results instead of inciting on an infinite scroll of results.
The apple music search is also atrocious - that gets a relook as well hopefully.
I think in general, we (or at least I) have underestimated how good Google is at search, probably a result of how they have been monopolising talent for the last several years. This technical superiority (particularly in the machine learning space) is going to be a huge advantage going forward, as already evidenced by how much better Google now is than Siri.
If this is the app that Apple considers the second most relevant result, I'm gonna say the jury is still out on App Store search.
http://i.imgur.com/5Lca7cw.jpg