Why does it show a wide "center" of a stud instead of a single point? Why are the "edges" 3 inches or more apart?

You're most likely over a double or triple stud. Double and triple studs (triple studs are much rarer) are installed around doors, windows, or anywhere the builder thought extra support was needed. Your tool's center-finding feature may detect a wide center zone rather than the center of double studs, but the edge finding capabilities will be unaffected.

Don't nail, drill, or screw anything into the center of a double stud — anchoring something between the beams won't give you the support of a normal stud center. If you need to attach something to a double stud, either use two screws or nails side-by-side for extra support, or find the center of one of the studs. To do that, use the edge-finding features and determine both outside edges of the double. Then measure in 3/4" inwards on either side (assuming your studs are the standard inch and a half wide) so you can targeting the center of one of the studs. While it's safe to nail anchor into the center of triple studs, make sure you use the edge finding feature over a wide range so you know absolutely where that center is.

If the wide center is accompanied by a WireWarning® detection or metal reading, there may be a pipe or conduit attached to the side of a stud. If at all possible, choose another stud in your wall to use so you don't damage plumbing or electrical systems.