Online Process Servers are connected to the Process Center and their status is available in Process Center Servers tab, also you can choose a snapshot in PC and deploy to it in an online manner, whereas a offline Process Servers definition may exist in the PC but is not connected or communicating with the PC, the process to deploy to them is offline also, you create a deployment package, extract the package from command line transfer to the target maching and with wsadmin commands deploy it. Also scripted deployments are recommended for actual Live environments.
You need to configure the Process Server with PC credentials, ports hostname etc to be able to make it online you can do this at installation of Process Server or later also.