Project unites boards related to one product, project or client. With Projects you can have an overview of your project, so you can collect Development board, Backlog, Timeline, To-Do List connected to it. Besides it Projects can be added to Timeline as a task, so you can have an overview of all projects. If the user is assigned to a project and boards are public to a project, they will see all it to the boards from this project.
Collection is boards grouped by certain criteria. For example, you can use it to group Timeline; Clients from different state or regions, by teams. The users will see the boards from the collection they have access to (for example, you have 5 boards in the collection and your colleague has access to 2 of it, he will see these 2 boards only).