Around 1995 (in the real world, time passes more slowly in the comic universe), Aunt May's health is even more precarious than usual, and Peter and Mary Jane are expecting a child. When suddenly Peter (dressed as Spider-Man) encounters a familiar figure:
The clone calls himself Ben Reilly. It turns out he hadn't died in the battle orchestrated by the Jackal, after all. He had just been knocked into a coma. He returned to consciousness shortly after Peter "discarded" his body. Some of the comics fill us in on Ben's experience after coming to:
Instead of confronting Peter, Ben had at that point snuck off and wandered the country for a few years. He's only returned to New York now because he heard that Aunt May was dying.
Eventually, Ben and Peter make a kind of peace, and Ben helps Peter fight crime, dressing himself not as Spider-Man but as the Scarlet Spider:
Then Peter gets sick and starts having what seem to be "memory flashbacks" as of floating in a clone growth tank.
How could that be? He tries to ignore these apparent "memories":
Peter and Ben then discover that the Jackal has returned... or at least a clone of him has. They race off to confront him, while Peter still worries silently about his "memory flashes":
(The clone of) the Jackal---in a snazzy new outfit---confirms Peter's fears by telling Ben he is the real one:
As Peter and Ben fight the Jackal, though, he keeps changing his story:
Then later:
Eventually, Peter and Ben persuade themselves that Peter really is the original, and Ben is still the clone. Like the clone of Gwen Stacy, Ben chooses to start a new life, away from Peter and the family and friends they both have memories of:
Mary Jane and Peter look at some slides from his childhood:
We'll stop following the story there. In the comics, things of course get more complicated. Peter gives up being Spider-Man for a while, and Ben fills in for him. Then Norman Osborne, the original Green Goblin, comes back (Spider-Man's enemies have a way of doing that) and ends up killing Ben. Peter and Mary Jane's life goes on.
If you really want to know all the details about Peter's interactions with Ben Reilly, you can read this Wikipedia article, or this 35-page summary.