I'm going to make a few assumptions and base the answer on them; The splatter is a paint splatter not a drywall mud based wall texture applied mechanically and the marks are from sanding with a course grit sandpaper, plus your original walls are smooth without any applied texture.
You have a couple of options;
1) The marks can be covered over with either drywall mud or spackling paste then sanded smooth. The area(s) should be primed before applying drywall mud, it could bubble when applied over paint.
Also, the repaired areas could appear smoother than the surrounding wall. To help blend everything use a "hot dog" mini roller with a thick floppy roller cover to apply the primer and work it to a fine stipple. A little drywall mud could be mixed into the primer for a more prominent roller stipple.
2) You could use a thick primer like USG First Coat. This primer can cover a world of sins and is designed for smooth walls. This is a good option if the entire wall is affected. USG First Coat is available through drywall supply houses and some paint stores.