A project is a place. A plan is a moment.
A project is where work lives permanently: the launch, the migration, the client. A plan is a decision about a stretch of time: this week, this sprint, this afternoon. Tasks belong to a project forever and to a plan temporarily.
What you lose by merging them
If a plan is just a project, then finishing the week means archiving the container, and the work that did not get done goes with it. If a project is just a plan, you end up with fourteen half-dead lists and no idea which is current. Both failure modes are extremely common.
How it works in practice
Publish a plan and it becomes a snapshot: what you intended, on the day you intended it. Tasks keep living in their projects. At the end of the week you can see the gap between what you planned and what happened, which is the only way anyone gets better at estimating.
The estimate problem
Nobody estimates well from memory. They estimate well from a record. Separating plans from projects is what makes that record exist without anyone having to keep it deliberately.