Note: This article covers submitting a project to a hackathon. If you are looking for how to create a project page, read this.
You can submit directly from the hackathon's Devpost page (for example, http://pennapps-xiii.devpost.com)
What is the difference between a project and submission?
When you create a project you are creating the project page that will house the details about what you're working on. When you want to enter that project as a submission to a hackathon that's when it is considered a submission. The two terms may be used interchangeably.
Whether you submit a new or an existing project, you will see a green bar confirming this: