Authentication with Unity Web APIs varies depending on their type.
Admin APIs are endpoints that allow you to reach Unity Services as an administrator of your Unity project. These APIs will help you configure services to run smoothly for your project. Admin API Authentication can be done through Service Accounts.
Client APIs are endpoints that allow you to reach Unity Services as the user of a Unity project. These endpoints will typically be called in the application (i.e. in game). Depending on the API, Client API Authentication be done through Service Accounts or Client Authentication.