Its exactly that -- seperation by way of radar.
Radar works in two ways - by showing a return of all objects struck by the radar beam (primary radar) and also by interrogating the transponder to display callsign, altitude, ground speed etc (secondary radar)
So because the controller can see the two targets, thier distance apart and thier altitude he can seperate them.
There are prescribed distances to seperate planes by horozintally depending by weight class and flight plan type.