Yes, it is possible to differentiate between a Facebook direct message and a Facebook post in Freshdesk. Unlike a ticket created via a Facebook post, a lock next to the Facebook icon will be present for a ticket created from a direct message in the ticket details page.
However, it is not possible to differentiate between direct messages and posts from the List View in the Tickets tab.
If you signed up before Aug 9, 2021, please click Previous plans to view your applicable plans.