A conservative person is someone who is clinging to an existing, though obsolescent norm. A conservative is fundamentally passive. He does not want to change, but when change happens, he simply adjusts his conservatism to the new norm.
A Right-winger is fundamentally active. He has a conception of what is right, of how things should be, that is based, not on custom, but on some idealization of the past. And his views, though in some sense backwards looking, are revolutionary.