Short answers, pulled from the story.
Social equality is a state of affairs in which all individuals within society have equal rights, liberties, and status. It can include civil rights, freedom of expression, autonomy, and equal access to certain public goods and social services. It requires the absence of legally enforced class or caste boundaries and an absence of discrimination based on an inalienable part of a person's identity.
Formal equality means equal opportunity for individuals based on merit. Substantive equality means equality of outcomes for groups, also called social equity.
The four standards are ontological equality, equality of opportunity, equality of condition, and equality of outcome. Ontological equality holds that everyone is created equal at birth, while equality of outcome argues that each player must end up with the same amount regardless of fairness. Equality of opportunity and equality of condition fall between, differing over whether people merely share the same rules or share the same starting point.
Ancient roots appear with the Stoics, Plato, and Aristotle, who rejected total equality in favour of hierarchy. Enlightenment thinkers including Locke, Rousseau, Montesquieu, Voltaire, Kant, and Wollstonecraft built a secular foundation. In the 20th century John Rawls, Ronald Dworkin, and Amartya Sen developed the contemporary notion, while Robert Nozick rejected Rawls' conception.
Major examples include the Abolitionist Movement, the French Revolution of 1789, women's suffrage movements beginning with the Seneca Falls Convention of 1848, and Japan's Meiji Reforms. Later movements include the Civil Rights Movement led by figures like Martin Luther King Jr., the Anti-Apartheid Movement led by Nelson Mandela from 1948 to 1994, and LGBTQ+ rights movements.
Social equality is variously measured through equality of power, rights, goods, opportunities, or capabilities. Economic development, industrialization, and education correlate with increases in social equality. Access to healthcare, social protection, democratic participation, civil rights protections, welfare policies, and redistributive taxation are also linked to greater equality.