I'd have thought a discontinued approach would only happen above the MSA, otherwise it's a go-round. A discontinued approach may follow the go-round (missed approach) procedure the go-round will (or should) follow the missed Approach at least until above the MSA.
Of course if it's daylight and good visual conditions a visual break off may be issued too just to complicate things... There are also complications of design such as parallel runways where a break-out procedure may be in place.
Vectors may not always be given on a discontinued approach and there would be no requirement for a discontinue approach to be issued exclusively by a radar unit; but the controller involved would be issuing some sort of tracking instructions...