What is the difference between App Store Connect and iTunes Connect app?
iTunes Connect is the marketing name for the originally released, Web based tool to manage app distribution on the App Store (iOS) and Mac App Store.

In June 2018, Apple rebranded iTunes Connect to App Store Connect and provided it as a separate tool:


Introducing App Store Connect


iTunes Connect is now intended to be used by content creators and distributors to manage media distributed via iTunes Store such as music, films, TV programmes and books, while App Store Connect is intended solely to manage app distribution for iOS (and by extension watchOS and tvOS) and macOS.

The separate iOS apps you see on your iPhone are focused on individual tools. You are able to see the app analytics in iTunes Connect apps as it was originally/previously used to manage app distribution.

This may remain so, till Apple completes transition to App Store Connect (or upto Apple's discretion).

Apple removes certain apps from search listing, (while still keeping them available on the App Store) while making transitions. You can still access the iTunes Connect app in the App Store using this link on your iPhone.