Let me tell you something you already know: there’s a difference between mobile searches and desktop searches. Even though the apps are identical and the search terms may be the same, users are not looking for the same result.
One example is maps. On a desktop, searching for a location on a map is like hypothetical research. The user is not quite sure where they want to go but they’re exploring the area.
On mobile, however, maps need to be much more decisive. Users are not exploring, they want to get somewhere. They don’t want to go through pages of results, they want the best match, it has to be nearby, and it has to be open! If I’m searching for a pharmacy at 11:30 at night, I don’t want the full list of pharmacies in my area, or even just the closest. I just want to see the ones that are still open. Yelp gets this and offers the “Open Now” option when filtering results. Google Maps doesn’t offer this option yet.
Another example of this is contacts. Pulling up contacts on the phone is not a theoretical friend-counting exercise or just maintenance as it may be on the desktop. I bring someone up because I want to call them. It is now 5pm. Is it OK to call my friend in Copenhagen? This is an easy question to answer: the phone knows what time it is and it knows where my contact is located (by country code at the very least.) Put the two together and warn me if I’m going to wake my friend up.
Bottom line is that mobile apps have access to more information about the user. Using that information can and should create a smarter user experience.