I must be confused (not unusual for me
), since I'm not clear on the difference. Can some kind person explain, please?
In both cases you gain more control over your device.
With iOS, the point is to break free of iTunes DRM so you can install apps not approved by Apple and not in their app store. You leave the approved ecosystem.
You don't need to root an Android for that.
Check one box in your settings to install unknown apps. You don't leave the ecosystem, you don't leave the Play Store, you simply get to access more apps in addition to the Play Store offerings.
Android is an embedded real-time Linux, a desktop operating system. Gaining root access is the same exact thing as gaining admin access on your pc.
When you root, you can modify areas that are locked away. You can turn on and control the Linux firewall, free. You can modify your button behavior (depending on the model). You can extend the ability to change the color theme of your device. And more.
You often - not always - need to be able to unlock your bootloader to root. HTC provides a simple facility for it, unless by contract Verizon or AT&T removes your access to that. I believe that the same is true for Motorola. The Google Nexus line requires installing some software on your pc, plugging in your phone, and issuing one command. Many of the Samsungs are rooter friendly.
The rest entail using exploits found by others. Some are easy, some are not.
Rooting and jailbreaking are similar in that you get more access, but they're not the same.
We're not in jail, we don't need to break out.