If you have followed this blog for a while you know how important I think the choice of words are. But the difference between assigning and picking tasks within a team might be bigger than than you think.
As it is pointed out in this article and organization where things are assigned tend to talk about people as resources while an organization where teams and individuals pick their works tends to be happier and hence more productive long term. At least that is my experience.
And since I tend to bring back examples from the military I would like to add one dimension to the argument. While the military sometimes have situations where you actually have to tell soldiers exactly what to do the most effective units do not get detailed instructions on what to do. They get a goal and pick their own path to solve that task.