There is a popular notion that agile is bottoms up and tradititional is top down. Neither is actually effective in deliverying value to the customer based on the needd capabilties, time phased to match the business or mission need.
The traditional - read PMI and an over generalization - project life cycle is requirements elicitaton based. Go gather the requirements, arrange them in some order that makes sense and start implementing them. The agile approach (this is another over generlaizaiton) is to let the requirements emerge, implement them in the priority the customer says - or discovers.
Both these approaches have serious problems as evidenced by the staistics of software development
- Traditional approaches take too long
- Agile approach ignore the underlying architectural impacts of mashing up the requirements