Here are the promised illustrations:
Direct democracy -
A group of animal rights activists in Hampshire, England discover that the local government is going to conduct a badger cull and after a brief discussion the activists find that they're all in agreement - something must be done to save the badgers. The group all sit down together and spend a couple of hours debating potential plans of action. After the proposed ideas have been discussed thoroughly, a leading activist, keenly aware of the badgers' impending doom, suggests that the group vote on the two most discussed ideas - going door-to-door with a petition to stop the cull, or publicly throwing blood on the farmers hired to hunt down the badgers. No one voices opposition to the suggestion, so they vote - 30% in favor of the petition, 70% in favor of public-blood-throwing-ambushes. The 30% minority reluctantly agree help out with the blood throwing because they were outvoted.
After the group all agree that something must be done to save the badgers, they sit down and brainstorm some ideas. After a long a tiresome discussion the group narrows it down to two potential ideas - (the same ones as above). The problem is that no matter how they approach it, a consensus cannot be negotiated over the two courses of action - there are some activists who just can't abide a petition, and others that just can't abide public blood throwing. Eventually someone says 'oh fuck it, let's follow the farmers around and when they spot a badger, jump between them and the badger', and at this point everyone's so tired of the endless negotiations that they agree human shielding is a good compromise.
Cynicism aside (sorry, I couldn't resist), the main difference between the two examples is hierarchy - in the first example, while every individual has contributed to the decision-making process, the way that they reach the final decision demands that those with minority opinions submit to the will of the group, which therefore becomes an authority over them. In the second example, the primary objective is finding a solution which all members of the group support - ie. reaching a consensus. This is less hierarchal in that no one is forced to do something they don't want to do.
Of course direct democracy and consensus are not mutually exclusive, many people view consensus-based processes of collective decision making as a way of organizing and legitimizing direct democracy. A lot of anarchists prefer consensus to other forms of direct democracy because it's less hierarchal, but some anarchists (myself included) are in principle opposed to consensus, although may well participate on their own terms, on a case-by-case basis. The problem with consensus is that it can still submit the individual to the will of the group, if it is assumed or demanded that members will not engage in activities - as individuals - that were rejected by the group.