Hi John Watermolen
I want to quickly piggyback off of Zahina's reply and provide a little clarification. If you wish to publish to a specific server from ArcMap, you can make a direct connection to that server and publish the service to the server by specifying that server connection. The only caveat is that it will not be a "hosted" service. See below:
How to publish a service from ArcMap—Documentation | ArcGIS Enterprise
When you are signed into Portal from ArcMap, and then you choose the option for "My Hosted Services (portalOrganization)" when gong to publish, then it will be a hosted service that resides on the hosting server.
In other words, you cannot specify which federated server that a service is published to when publishing to Portal from ArcMap, but you should not need to since ArcMap gives you the option to publish directly to the server anyway, regardless if it is federated or not.
ArcGIS Pro does not give you this option and can only publish to a server if it is federated with Portal and that is the Portal your are signed in to.
Does this make sense?
-Daniel