They're far more than minor details of project management. Compare and contrast "Waterfall" with "Agile". The first says you develop an exhaustive specification of what you want, then pass it through channels, and only at the end do you work on coding the whole project to spec. The later says you start developing, and it's a back-and-forth process defining the end project spec along the way, based on what is found to be practical in writing the code.

In fact, just visit the "Criticisms" section on each method for a quick breakdown.