What are the differences between these two?
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Platformers have the player sprite move. Scrollers have the 'stage' sprites move.
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Platformer games is where the player sprite actually moves, scrolling has the effect the player's moving, but it's actually just the background sprites.
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The explanations above pretty much cover it.
The advantage of a scroller is that you can have bigger playing areas (larger than the screen since you can scroll) but they are harder to make.
Here are examples of the two different types, taken from my latest games:
Scroller
Platformer
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