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That might be it...! I'll look up some YouTube videos to confirm. :)

No, that's not it... The game I played was top down, like Galaga; your vehicle stayed at the bottom mostly, while the screen scrolled upward.

There's two Genesis (or maybe SNES) games I rented a long time ago, that I have forgotten the names of:

One was a top-down shooter. I think you pilot a helicopter, and can get powerups...

The...