Redsn0w provides both of these tools to jailbreaking iDevices. You can see not only Redsn0w but also other jailbreaking tools are also using tethered and untethered methods for their tools. But most of users are do not know the difference between them. This will simply show some information for you.
If you are using Redsn0w tethered jailbreaking tool you need to connect the device into computer when reboot the jailbroken device. Because iOS hardware needs computer connection to boot the device. So when you are using tethered jailbreaking method it will clearly show this step once you boot the device. (This will show while jailbreaking using tool).
This is the opposite of tethered jailbreaking, that means not need to connect your device into computer when reboot the jailbroken device. Because iOS hardware not needs computer connection to boot the device.
We can see some jailbreaking methods is mixed with tethered and untethered methods. This is semitetherd jailbreaking. In this method you can reboot the device without computer connection but some functions disabled like you can not run Cydia. These functions you can do with computer connection.
untethered jailbreaking method is useful because it is user friendly. Some person’s are waiting till release untethered jailbreaking method. But semitehtered and tethered jailbreak methods are also useful to jailbreak our devices.
This software support for Windows and MAC platforms. Redsnow tool provides tethered and untethered jailbreaks according to iOS and it support following iOS with the device. Following diagram clearly show relevant with the iOS version.