Tickets have one department. A single email opens or updates one ticket.
Sending the exact same email to multiple ticket inboxes will result in a single ticket. The second one will be dropped as it is in fact already a ticket. The email(s) share the same message-id, subject, etc. So they are duplicates.
If someone wants to open two tickets (for the same issue) then they will have to send two emails. One to the first address. Then another to the second address. I would recommend that they not have the exact same subject also.
If you want a ticket to be accessible by people from more then one department then you would use a Team.