Project Management Body of Knowledge.
PMBOK® is a generic term to define a collection of all knowledge pertaining to Project Managemnet. This may be published material or unpublished practices also. e.g. This includes a specific process or processes in your own organization pertaining to Project Management.
The PMBOK® Guide to 4th Edition is merely a sub set of PMBOK®.

Project Management Institute.
PMI is a non-profit professional organization promoting the profession of project management.
Website URL - www.pmi.org
PMI offers certifications such as PMP, CAPM, PgMP, PMI-SP, PMI-RMP and its own version of agile project management.

Project Management Information System.
PMIS is a generic term used to indicate presence of any or all tools, software or otherwise, that can facilitate project management. Examples: Any of the project management software like dotProject, MS-Project, Primavera etc. It could also include defect tracking or bug management systems , status report generation tool, Resource Assignment or resource management software, Repository for Project documents,Change and configuration management software etc.

Project Management Professional.
PMP is a professional credential for project managers offered by PMI - Project Management Institute, USA.
This certification is the most recognized by the project managers of any industry , around the globe.

Product Life Cycle generally consists of sequential phases as required for conceptualizing, manufacturing and maintaining the product. The last phase generally being retiring of the product.

Project Charter is a document that formally recognizes existence of a project and authorizes resources to be allocated to it.
It is distributed or issued under the aegis of an external senior manager , also known as Sponsor. Sponsor controls the funding for the project.

The term is used to define the collection of the many documents and outputs of various processes and project execution. Project Documents assists the project manager to plan and take project decisions. These include (not an exhaustive list)
Requirements documents and traceability matrix,
Stakeholder Register,
Activity Lists,
Risk Register,
Schedule data,
Cost estimates and Basis of estimates,
Responsibility Assignment Matrix,
Quality Audit Reports,
Training Plan,
etc.

A set of project phases generally executed sequentially. Output of each of the previous phases are used as inputs to the subsequent phases. This is a logical way of breaking the project into manageable pieces.

It is important to understand that Project Life Cycle and Process Phase groups are very different. In fact in each phase of the life cycle one or more of the process groups' processes are performed

The application area dictates the type of project life cycle that should be used.

For example SDLC or Software Development Life Cycle is used for Software Development , Construction Industry would have their best practice life cycle etc.

Product life cycle is different from project life cycle

This is a master plan for the project. Project Management Plan includes all the baseline and subsidiary plans from various other processes like the
Scope Baseline, Cost baseline,
Schedule baseline,
Quality plan,
Risk plan ,
HR Plan,
Communications plan,
Procurement plan etc.

If you want to know what needs to be done in a project and how , then refer to the project management plan.

Purchase or acquire resources in terms of products, services or results that are required for the project. Includes leasing or renting also