"The Hawk and Dove" is a nice tavern on capital hill in DC.
Hawks favor war, doves favor peace. One can be generally hawkish, or dovish, or, one can be a hawk on Iraq, and a Dove on Bosnia for instance. It is not a great system for labelling. One irony is that almost all generals oppose almost all wars. Should we really label them doves?
Left-wing and right-wing are generlly the extremes of liberal and conservative, respectively. It is a bit clumsy, as there are multiple facets to what makes one liberal or conservative. There are also big issues, like trade, which defy labelling.
Njorl