I don't use/have never used a PID (Project Initiation Document), but as for the others, they are different. In my line of worK:
The Project Proposal is a document written by a hopeful contractor to a customer as part of a bid for work. It typically includes 3 major sections:
- Technical proposal
- Management proposal
- Cost Proposal
Depending on the size of the contract a proposal can be anywhere from 5 or 10 to thousands of pages long.
The proposal may also be required to contain a 'separable SOW' - a completely self-contained statement of work that the contract will perform to after award.
The Statement of Work defines at least the goals, scope, period of performance, milestones, major activities, and reporting requirements. It may also define quality, compliance or performance standards, security requirements, financial reporting requirements, travel etc. Depending on the size, complexity, and type (fixed price, cost plus) of the contract, the details of a SOW can vary wildly.
The statement of Work is typically more than 3 - 5, but less than 20 pages long.
The Charter can be defined in several ways, but if working on a project that already has a formal SOW, it can be as simple as a document that formally associates a specific project manager with a charge number and a statement of work. It formally authorizes the PM to use the defined charge number to plan & execute the project.
A charter is frequently 1 page.