What does “social realization” mean, and what source supports it?

Social realization means:

the extent to which people are actually recognized and treated as social equals in everyday social relationships and institutions.

It is different from economic realization.

Economic realization

Can you:

• acquire land?
• obtain capital?
• earn income?
• establish an independent livelihood?

Social realization

Are you:

• recognized as a social equal?
• permitted to participate in public life as an equal?
• treated with equal dignity?
• accepted as belonging to the same civic community?
• free from socially enforced racial hierarchy?
• able to participate in schools, public institutions, and other social spaces on equal terms?

The evidence for the post-emancipation United States is quite strong.

The Library of Congress documents that African Americans initially gained new political and social opportunities but that opponents later worked to erode those gains, with segregation, racial violence, and other forms of subordination developing during and after Reconstruction.

More theoretically, Rogers M. Smith distinguishes “legal citizenship”—equal legal rights and duties—from “lived citizenship,” which involves sufficient economic, political, and social standing to be treated as civic equals.

That source is particularly useful for your conceptual distinction.

You could therefore write:

Rogers M. Smith (2022) distinguishes legal citizenship, understood in terms of equal legal rights and duties, from lived citizenship, which requires sufficient economic, political, and social standing for people to be recognized as civic equals.

This is not specifically a study of emancipation, so use it for the conceptual distinction, while using Reconstruction historians for the historical application.