There are different project management models. Across this whole web site we use the project management life cycle as presented in the section The Fundamentals of Project Management. It is a linear process model consisting of four phases.
In this picture it looks as if the four phases did not overlap. In real life, they often do but we simplify for the sake of clarity of our presentation.
This project management process model with non-overlapping phases corresponds in fact to the waterfall model of which you find a small case study here.
The waterfall model is based upon the principle that one phase cannot start until the previous one is completed. For example, in a typical construction project, we cannot start implementation phase until approval of all planning documents is done, i.e. planning phase is completed. In fact, to one extreme, this model does allow for overlapping phases, in that one phase cannot be finished until the previous one is finished.
In contrast to this linear model, we have an iterative model, the spiral model of project management.
The spiral model is based upon the principle that we go through the different phases again and again, until we reach a certain degree of maturity of the product to be created which e.g., a customer can accept. It is even possible that one part of our project is still in definition phase while another one is already in implementation phase. Typical examples of this iterative approach would be IT projects, i.e. the design and development of products and services in the IT industry with its short innovation cycles and high probabilities of changing requirements during implementation phase. See also the sub-section Managing IT Projects.
Most of our real life projects seem to be mixtures of these extreme approaches, with some sub-projects following more the waterfall model principles, others following more the spiral model principles.