An independent terrorist actor works outside of a command structure, and is unaccountable to the claimed collective cause of a terrorist group. They are often active due to the motive of vendetta or seeking personal gain.
This was true in the case of Vietnam, where the US government undertook a large terrorist operation to exacerbate the pre-existing civil conflict in Vietnam, unbeknownst to the larger American public (the cause which the public was led to support was "anti-communism"). Also the Omagh bombing in Ireland, where the "Real IRA"—a splinter group from the more conciliatory IRA, killed 29 people in a bombing attack against Ulster Loyalist families—a completely radical action, according to the mainstream Republican view.
In the Palestinian territories, a similar (but more complex) situation exists where in addition to the large organizations there are several distinct factions (mostly based on clans and blood ties), under constant pressure by retaliatory actions from Israel, tend to be extremely divided about any immediate course of action—such that they can rarely or never act in a collective or controlled manner. Under stress, the choice between action and inaction tends to default to one between violence and protest. Violence, being far more decisive than moderation and discussion, tends to win out over discussion.
Other examples are: