A Competitive Task is one in which two or more people are competing, but are unable to directly affect each others' chances of success.
For example, a no-contact footrace, or a poetry competition.
Simply enough, everyone involved rolls, and whoever gets the greatest difference under their TR wins. It's often not necessary to go on and determine the actual Quality Level of the winner's success, unless the Ref wants extra detail.
A Resisted Task is one in which two or more people are competing, and they can affect each others' chances of success. For example, a swordfight, a chess match, or a comedian dealing with a heckler. Again, everyone involved rolls. The winner is the person who got the greatest difference under their TR. But this difference is reduced by the amount that the loser succeeded by. (If the loser didn't succeed at all, there's no reduction).
With Resisted Tasks, it's often useful and necessary to then use the adjusted difference to determine the winner's Quality Level; this will give damage inflicted in a fight, for example.
Almost any kind of task can benefit from a little help, whether competing or otherwise. A team makes one roll, using the best tr amongst them. Each person helping adds 3 to this tr.
Note that the Ref should feel free to disallow aid from people who just aren't very skilled at the task in hand, and may also state that there is a maximum number who can help each other before they start getting in each others' way - like trying to knock a door down together, for instance.
The Ref always has the option of applying modifiers to a Task Rating once it has been determined. Distractions, poor equipment, injuries, hasty work and any number of environmental circumstances can affect the chances of success. Negative modifiers make the task harder, while positive ones make it easier.
Note that modifiers can lower the TR below 1, or raise it over 20. If the TR drops below 1, the task is impossible under current circumstances. If it goes above 20, the task will automatically succeed; there's no need to actually roll, unless the Ref wants to determine a Quality Level. There's no hard-and-fast scale for modifiers; there are too many possible combinations. But the Ref should bear in mind that a + or - 4 makes a big difference to a 1d20 die roll.