Earlier quoted context omitted.
No, they are exactly the same. Despite what Apple marketing would like you to believe, the search app collects the same information when you perform the same actions on both devices.
"the search app" Genuinely - what's this on iOS? I don't recall ever having used a "search app" on my iPhone.
Just as there is a Google search app on Android (https://play.google.com/store/apps/details?id=com.google.and...) there is a Google search app on iOS. They collect the same information when you perform the same actions, though many irrationally believe otherwise.
Similarly, the Google search web app collects exactly the same information on both platforms.