Root Access - root access is a way of providing an executing user or software with the ability to run any program they want on the operating system.
Jailbreak - jailbreaking allows users to change their device outside of what the device was designed for by the vendor. iOS devices are more challenging and restrictive to jailbreak than android devices.
Other Notes
When you jailbreak devices or provide root access you are bypassing built-in security systems which were made to protect the device