What is the difference between "add" and "edit" privileges for repositories?

The "edit" privilege allows HTTP PUT requests, and the "add" privilege allows "POST".

Most build client tools that interact with Nexus Repository deploy content via PUT requests, but there are a few exceptions, such as Python.

The simplest thing to do is not to worry about the above, grant add+edit to anyone that needs to deploy artifacts and use the repository's deployment policy to control whether components can be updated.

If you don't want to allow overwriting artifacts in a repository that should be done with the repository's deployment policy, setting it to "disable redeploy".