parse-server is the raw Parse Server module itself
parse-server-example is an application in which Parse Server is added as a sub-module, which gives you space to code an application around Parse Server
To kick-start creating your own Parse Server application we created and recommend the parse-server-example repository.
As analogy, if you eat out in a pizzeria, you likely wouldn’t go to the oven and philosophize with the pizzaiolo about the dough (although that can be good advice sometimes).
Instead you would:
sit at a table (parse-server-example application)
talk to the waiter (npm)
order your pizza (already added parse-server module)
order side dishes (other modules you may want to add to your application)
enjoy the bread sticks already on the table (already added modules for code testing, code quality)