Hi Isaac,
as Jocelyn has already mentioned, you can only have one start event. The start event is always triggered by a call to a web service. As your process is not designed, yet, I'd suggest to design a web service interface that can be used in both situations. If you want to know from where the process was started, include the department (A or B) in the interface definition and fill it when calling the interface. In this way you can also handle differences in the process by checking the department in an exclusive choice gateway.
If the interfaces have to be different, e.g. because application A and B call different interfaces already, you could investigate the usage of iFlows with a mapping step to map the interface from application A and application B to the interface used in the BPM process.
I'd definetly not recommend to implement two very similar processes because they will have to be changed both if you discover a bug in one of them.
Best regards,
Frank