Create First Project
In a Azure DevOps Organisation you can have multiple projects. It is best to think about these project around a Product or a actual Project with a fixed delivery.
You Project Tasks, Test Scripts, Source Code Repository, Build and Release scripts will live in this Project.
What is the difference with Public vs Private Projects. Private means you can keep the whole project under lock and key so no-one else can get to it unless you grant them permission. Where as Public as the name may suggest is open for anyone to access, as long as they know the URL. The other benefit a Public project has over Private is you can have unlimited hosted build agent minutes and 10 Parallel.Compare to 1800 minutes per month and 1 free self hosted agent
TIP
You can have a central policy to only allow Private projects to be created.