Alternate Mode is by far the more commonly used mode, typically allowing you to play your selected Mix on any of three monitor pairs (or other devices)
Independent mode is usually used for multichannel outputs - typically 5.1 surround in which the three mixes can be sent simultaneously and seperately to the outputs. It can also be used for more involved mixing, especially mixing OTB and when using many external effects.
The following link will explain how it is set up . it is perhaps not so obvious.
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