What you have installed is a Private Security Gateway. What is in CMC is for the Public Security gateway. See info on both in links below
Public SG -
Please let me know if you have any further questions
So If I understand you correctly, the thing that differentiated between a Private SG and Public SG isn't just a matter of configuration difference in their config file is it? It has nothing to do with whether you installed it in DMZ or not, or whether you installed it with any special parameter when executing the installer in cmd is it?
Correct. The installation parameters are different, binaries are the same. But you cannot switch the installed private SGW to the public one or vice versa. So if you need public gateway instead of a private one, you will have to reinstall it. The public one is downloaded from the cluster management console of the Dynatrace Managed and the private one is downloaded from a tenant (particular environment).