I assume you are talking about Group Wildcards and Private Wildcards as well as private call radio IDs vs Group IDs.
Talk Groups are "channels" assigned to departments, specific areas, specific squads, specific tasks - Blah PD, Blah FD, Narcotics, Records, Etc. Typically, more than one radio is assigned to a talk group. A transmission can be sent to a specific talk group so that only the members of that talk group hear the transmission on their radios.
A private call is one from one radio to another radio. One user on the system makes a private call to the radio of the other person, and nobody else on the trunked system would typically hear that.
If you add a group wildcard for a trunked system, this means you'll hear ALL activity from ALL talk groups on that system without having to program in each and every talk group. This is very useful for a new system that just came online for which nobody has a record of the talk groups in use. You'll see the talk group ID when there is a transmission and you can note who is talking on it and possibly determine what the talk group should be labeled if nobody has already documented it.
If you add a private wildcard for a trunked system (one that supports it / has this feature enabled for their users to use), you'll hear private calls between two radios. You'll see the radio IDs and can add them and label them (in the case of a PSR-500/600 and maybe some other PSRs).
Not all trunked systems have the private call feature available/enabled for their users. On our county system, I have never heard a private call - it may be that nobody knows how to make one, or it may be that the administrator of the system specifically prohibits private calls or that the system just doesn't support it. The Ohio MARCS statewide system, for instance, does have private call ability. Those who know how to use it [and I'm guessing who are authorized to use it] can make a call from their radoi to one other specific radio and nobody else on the system (except us lucky ones listening with a scanner) can hear it. Users of the multistate AEP EDACS system are always making private calls.