The labels are not useless, they represent certain values and disagreements over how society should be governed. Of course, each of the values has a failure mode, but they are different. The values are:

- Right-wing, conservative, authoritarian - society should be governed by elites, conflict should be resolved by submission to authority

- Left-wing, socialist, democratic - society should be governed by equal peers, conflict should be resolved by democratic consensus

- Liberal, individualist, pro-freedom - the question of societal governance (and the arising conflict) should be avoided if possible by giving each participant their own life independent on others

Of course it is confusing because people cheat and do not always want to state their aims clearly. The values are also not opposites, but independent; they can also be applied per problem. For example, most famously, some communists were both left (they wanted a socialist society without classes) and right (they wanted the transformation under the party authority). But each pair of these has a similar conflict like that, so (aside from the communist spectrum above) you get also capitalist spectrum between right vs liberal, and anarchist spectrum between left vs liberal. In the middle of all 3, things are roughly social-democratic.