What's the link between the different games in the Far Cry series?

I couldn't find any "confirmed" links, aside from "wide beliefs" that the first game's protagonist is the second game's antagonist.

Clint Hocking, Far Cry 2's Creative Director confirms the above fan speculation in the Oct. 2021 IGN article, How Far Cry's Iconic Villains Were Created (emphasis mine):

...But beyond the game’s story, there’s a fascinating history behind the Jackal that few people outside of the walls of Ubisoft know.

“The Jackal is actually supposed to be Jack Carver from the original Far Cry,” Hocking reveals, confirming a long-held fan theory. Both Carver and the Jackal have a history in the US Navy, and – perhaps most tellingly – some texture files for the Jackal in Far Cry 2 are named after the original Far Cry protagonist. These details have convinced some fans that the two characters are related, but Hocking’s confirmation finally transforms the theory into fact.

“Jack Carver in the original Far Cry was this shifty, smuggler, gun runner kind of crook,” says Hocking. “The idea was [the Jackal] is just him, 10 years later or something, after he's seen whatever he saw on this island [during the events of Far Cry]. Maybe it was drug induced, maybe it's post-traumatic stress disorder, or maybe it's real. But the idea is, a decade later, he has leveled up his smuggling game, and he's gotten embroiled in this conflict. But he's also been through a lot more and he's seen a lot of messed up stuff.”

This fascinating origin story is, sadly, nowhere to be seen within the world of Far Cry 2. But despite his link to the original Far Cry only existing within the minds of the people who made him, The Jackal’s warped moral compass makes him a great villain in his own right. Compared to the bad guys who will succeed him, though, The Jackal’s role in Far Cry 2 is relatively straightforward.