I didn't have any involvement in the technical setup of the badges nor in the name choices.
Unfortunately the administrative interface doesn't provide any useful information about these badges:
From what I can see, the award mechanism and the award criteria are not accessible to an admin.
I only know the information that was already shared in the thread:
"Old forum" is referring to the SMF framework in use up to 2021. Here is the description of the post count criteria in place in SMF:
I will see if I can get access to the criteria and definitive namesakes for the current badges.