Social Republicanism is a moderate form of Authoritarianism.
Republicanism describes what is more commonly called a representative democracy; it restricts the term "democracy" to refer only to direct democracy.
For these reason, the primary difference between the Social Democracy and Social Republicanism is that later's attachment to preserve existing class structures and delineations.
People who fall in this category tend to be moderate conservatives in most countries around the world (except for the United States, which is more Capitalistic). Parties that fall in this category tend to refer themselves as republicans,