As mentioned in the above answers are certainly precise. Use a Project Site if you want a Task List tied to a Project Timeline view. If you don't need a timeline on your site landing page (or wherever else you might show a task list) then you can always just add a Task List app.
In practice the only real difference is which features are turned on by default. Any Team Site can quickly be turned into a Project Site by activating the Project Functionality and Site Notebook features in the Site Features (/_layouts/15/ManageFeatures.aspx)
Note - you'll need elevated permissions to access the Site Features