Different Spiderman. It's rather tricky, considering the way marvel has thier multiverse set up. 616 is the numerical designation for the mainstream canon occurances of events.
So while that joker joker may have encontered something like 9205 Spiderman the first time, it might have been like 9615 Spiderman the second time. Since the two spidermen would have bee identicle, much like encountering someone's twin, you'd remember meeting the first sibling, but the second sibling would have no memory of you.
That spidey was a clone of the normal spidey. His name was Ben Reilly, he didn't know him but peter did. Although I still don't get how spidey got to gotham city in the spider-man and batman comic, how did he get from one universe to the next?
Only the recent Avengers/JLA seems to change this; they met for the (seemingly) first time, and that it's a recognized event in the history of both Universes, aka its Canon.
All previous crossovers, the atitude has either been they have shared this world the whole time, or the meetings & memories ultimately get wiped from existence aka DC/Marvel All Access.
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"I'm not smart so much as I am not dumb." - Harlan Ellison