Test Planning is the action of discovering how to investigating a particular product – or a part of one.
I have written about Test Planning Ceremonies here.
The goal of the planning activities is to produce a test plan (see below). The process of such a planning is obviously contextual and, thus, the best ways to do it will be discovered by experimentation.
A Test Plan is the result of a test planning session. It consist of action to be taken, artifacts to be collected and produced, procedures to be followed, results to be presented, etc.
The exact content – and the format -of a test plan is contextual to the stakeholders (testers, developers, managers, clients, etc) and the product in question. During the planning, the needed content is discovered throughout talking and experimentation.