The detailed, most popular version of the Osiris myth that I give in my article on Osiris derives mainly from Plutarch, but there are much older, Egyptian sources of the basic myth. As far as I can tell, the consensus of Egyptologists is that Osiris died and was brought back to life. His rebirth came in several forms: (1) Isis as a bird fanned life and vitality back into him (perhaps concentrated in his semen, as a symbol of life); (2) Osiris lived on in the Underworld as part of the cycle of pharaohs' and eventually everyone's rebirth; (3) he lived on through his son Horus who went on to avenge him against Set.
Now, if we’re talking about whether any of this amounts to a resurrection that’s close enough to Jesus’s resurrection to support the Christ myth theory, I’d say the Christian apologist has two big problems. First, she confuses identity with similarity. What matters is the ideal type of a deity brought low and vindicated as represented by a triumph over a fearsome enemy, such as Set or death itself. I explain that ideal type in “The Mythic Core of the Christian Narrative” (first link below).
Ancient Egyptians were obsessed with death and resurrection. They preserved their bodies as mummies because they thought they were needed in the afterlife, and the Osiris myth is supposed to justify that practice. Isis used magical powers to reanimate Osiris.
The reason that’s close enough to Christianity’s founding resurrection story has to do with the second problem, which is that Jesus, too, doesn’t tarry in his resurrected form, nor is that form so unambiguously physical. Some gospels emphasize the physicality of Jesus’s resurrected body, while others show that that body had magical powers. The earliest accounts were Paul’s and he said flesh and blood can’t inherit the kingdom of God (so Christians needn’t worry about inheriting gross zombie bodies). Jesus’s resurrected body was therefore spiritual—just like Osiris’s in the Underworld.
Jesus doesn’t remain for long on earth after he died, but swiftly ascends to a higher plane—just like Osiris who lives in some capacity just long enough to conceive Horus, his instrument of vengeance. Jesus, too, will return in the Second Coming and bring divine judgment. Just as Set betrayed Osiris, Judas and the Jewish elders betray Jesus. And so on.
Regarding Mark’s empty tomb story and whether he made it up, see Carrier’s “Why Did Mark Invent an Empty Tomb?” (second link). The story comes from the psalms, like much of Mark’s passion narrative, and from his riffing on Paul’s theology.
