When managing log sources on a LogLogic LMI appliance you will see on the Management->Devices page a tab called Device Groups. On that page is a field called Group Type. There are two possible values for this field. The value is in the context of whether the groups exist on an appliance configured as a Management Station.

A "Local” group contains only devices that are configured on the local appliance. In fact, on an appliance that has not been set up as a Management Station the "Group Type" will be grayed out and all groups will be "Local" by default. You can have a local group that exists on multiple appliances with the same name. This occurs automatically for the default device groups but applies equally to custom groups.

 A "Global" group is created and exists only on the Management Station and contains devices from the MS appliance and any other appliances configured as members of the Management Station cluster.