Tethered Jailbreak vs Untethered Jailbreak
Jailbreaking is a method to get full access to Apple devices like iPhone, iPad, iPod Touch and Apple TVs. Basically it’s like getting Administrator access in Windows platform and root access in Unix/Linux platform. Jailbreaking is a process to get full access on Apple iOS (earlier Apple OS) to overcome the limitations imposed by Apple. Even if you jailbreak still Apple devices can perform its normal functions on top of removing the apple limitations.
What is SIM unlocking and What is Jailbreaking? Once your Apple device is jailbroken it will work with any carrier. SIM unlocking is one of the features of Jailbreaking. Apple sells unlocked phones; they also work with any carrier. Else even if you are locked with a carrier, still you can call carrier support centre and ask for SIM unlocking for a certain period if you are going overseas.
Tethered Jailbreak
In Tethered Jailbreak the device need to be connected with computer each time the device restarts while in the process of Jailbreaking. On each steps of Jailbreak when the device restarts , it needs the Jailbreak application which is running on the PC to restart.
Untethered Jailbreak
In Untethered Jailbreak, the Apple devices need not to be connected to PC except to start the Jailbreaking process. Even if the battery dies during the process , you can charge and reboot the device. But its always better to start with fully charged devices.
Note: However Apple has not recommended Jailbreaking process.