I'd have to look it up to see which was first, but the ports of Pitfall! are a rough contemporary of Spelunker, which also has an infamous NES port. Both are Western-originated games about descending into caverns and collecting treasures. Spelunker in arcade is actually really interesting in how forgiving it is relative to most platformers of the time, while the NES game is its merciless counterpart.
It was probably Pitfall II, I thought the same as you, but looking around the only arcade game I found was Pitfall II, maybe we played some kind of bootleg but I can't find anything about it either.
Before now, I never realized that it was (sort of) the first platformer/side scroller.