An aircraft can have only one heading. When you look on the dash, the compass will provide it. The way the aircraft is pointing, measured in degrees magnetic.
The confusion arising is the phrase 'radar heading'. If you are flying under your own nav, you are flying a heading to make good a track. That heading will vary for wind etc. When a controller talks about a radar heading, she means 'disregard your track just look at the compass and fly according to the magnetic heading that I tell you.' The 'radar' bit is just emphasising that you are under radar control. It actually has no meaning. The pilot then picks this up, and on transfer reports 'radar heading ...' to emphasise that he is on a heading not necessarily of his choice ie. not making good a track.
When you get the 'report heading', then 'make that a radar heading' thing, the controller is just making sure that you continue going across the screen in a straight line. Your heading is making good a track, and though the controller doesn't really care about the track, locks you on that heading, taking responsiblity for nav off you, to keep you going in a straight line across the radar for his purposes. In other words, giving you a vector without taking you away from where you want to go.