iPhone no jailbreak is a concept using for stock iPhones which is using orginal untouched iOS version. On the other hand iPhone jailbreaking is the removing of software restrictions imposed by iOS, Apple's mobile operating system, on devices running it through the use of software exploits. These devices are the iPhone, iPod touch, iPad, and the AppleTV 2 and 4. Jailbreaking permits root access to the iOS file system, allowing the downloading and installation of additional applications, extensions, and themes that are unavailable through the official Apple App Store. However you update your phone with latest available iOS version, the jailbreak process deletes itself and the phone returns its past settings. Currently the latest stable jailbreak works for iOS 9.3.3 and lower versions. if the jailbreak not suit your needs you can use monitoring app on stock iPhones (no jailbreak) with all original iOS versions.
Rooting is the process of allowing users of smartphones, tablets and other devices running the Android mobile operating system to attain privileged control (known as root access) over various Android subsystems. As Android uses the Linux kernel, rooting an Android device gives similar access to administrative (superuser) permissions as on Linux or any other Unix-like operating system such as FreeBSD or OS X. After rooting process if you want to unroot your device again you should download SuperSU app on playstore. After opening the app go to Settings > Cleanup > Full Unroot option then after restarding your device will return past settings. Of course there are many methods to unroot your device again. if you do not want to do root process you can use monitoring app on stock Android devices (rootless) with orginal Android 4+ versions.