Actually, both “liberals” and “conservatives” use both, it is not that cut and dry.
Also, in relation to the abortion, Sunday Obligations, contraception, and hell and damnation not getting their “fair share”, it comes down (IMO) to an fear vs self determination approach.
The examples you mentioned come from a theological approach to “scare people straight” for motivation. While it can motivate for a while, it can also be self-defeating as time goes on as it is has strong de-motivating undertones as the fear sets into people’s psyche.
The Social Justice theology is popular with a self-determination approach. It adds a second dimension to people’s faith by having them live it in a positive way to turn what is seen as a negative in life into a positive. Both the helper and the helpee both receive an uplift from these actions. Instead of looking at the world as a fearful place, it makes the world a better place in small ways, which accumulate quickly.