If you add a new domain alias, each user in your domain automatically gets an addition email address that they can receive mail at. The image shows how this would work if your primary G Suite Domain was kitbeat.com and you added mixosteps.com as the domain alias
If you add a new domain, it allows you to add different users at different domains. This is ideal if you are running a G Suite domain for a multi academy trust, or you wanted to setup a separate domain for governors for example. NOTE: You can still add domain aliases to individual users when a domain is added in this way.