A swedge is a bevel ground along the top edge of the blade near the tip, thinning the spine without sharpening it. It reduces the mass behind the point so the knife penetrates more easily, and it is left blunt.
The two words describe the same physical grind and are often used interchangeably. In careful usage a swedge is purely a taper that is never sharpened, while a false edge is the same grind taken to something closer to an actual edge, sharp or not.
A swedge is most obvious on a clip point, where the clipped area is often swedged, and on spear point blades.
Removing steel from behind the point makes the tip narrower in cross-section, so it enters material with less force. It also lightens the front of the blade, which shifts balance back toward the hand.
The cost is tip strength. Less steel behind the point is less steel to resist bending. A heavily swedged tip is not the one to pick if you expect to lever or drill with it.