Using heading on its own could be misunderstood.
To me a heading is the way the aircraft happens to be pointed and in the absence of other constraints the pilot can alter it to suit his or her navigational needs
A radar heading is a heading assigned by a radar controller and the pilot should not alter it until released from it by a radar controller.
As has been pointed out, the reason for advising that an aircraft is on a radar heading on first contact is because some sectors don't co-ordinate such instructions (and effectively are getting the pilot to do it for them) or because controllers are only human and may simply forget!