Wallpaper/drywall damage

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I'm removing the dark green kitchen wallpaper to paint it light yellow. It was placed on untreated drywall and I have many brown paper patches that must be repaired; however, I'm a complete novice at this! What's the difference between spackling and joint compound? I know the compound should be spread thinly to even out the surface, but do I have to scrape off every single stray millimeter of adhesive before I do it? Is this skimming process sort of like spreading frosting on a cake?