Untethered-- The normal jailbreak, the device with function the same except it is jailbroken. It is best to have an untethered jailbreak
Tethered-- Each time you boot your device or restart, it will be stuck at the Apple logo. In order to fix this is to go to the program you used to jailbreak your device (i.e. Redsnow) and click "Just Boot Tethered" to boot your device. This also means that if you install a Cydia app and it says "Reboot Device/Restart Spring Board" then you will be stuck at the Apple logo.
Semi-Tethered-- Same as tethered except when your device runs out of battery, the device crashes and reboot into a semi-functioning stage. This is good especially if you don't have a computer with you.You can use Phone, SMS, and other apps. You cannot use Safari, Cydia, Mail, or Jailbroken Packages you've downloaded. They will crash. (You can use alternative web browsers like Opera Mini or Google, they will not crash.) To download Semi-Tethered, visit How To Download Semi-Tethered.In order to get it back to normal you must to do the same thing you do to tethered.
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