I originally thought to not upload the Easy run, but I think the differences are both interesting and hilarious, so I opted to keep it instead, for documentation sake!
The main difference between Easy and Hard, weirdly enough no Normal, is Stage 5, 6, and 7 got skipped. After Stage 4 boss, you get to fight the final boss, 2 of them at the same time, but not the true final boss. Arguably the final fight is harder in this route, but you still can hoard more lives here because of the skipped stages, at least. Also seems like the fire rate of the enemies are lower in Easy? But it's rather intangible. If you don't feel confident yet with the Hard course, trying out the Easy course first is suggested.
One thing for sure that is not different is the ending. Those who wrote that the endings are different, in particular on Wikipedia, if you call yourself a journalist I really question your professionalism.
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