Economic inequality is an umbrella term for three concepts: income inequality, how the total sum of money paid to people is distributed among them; wealth inequality, how the total sum of wealth owned by people is distributed among the owners; and consumption inequality, how the total sum of money spent by people is distributed among the spenders. Each of these can be measured between two or more nations, within a single nation, or between and within sub-populations (such as within a low-income group, within a high-income group and between them, within an age group and between inter-generational groups, within a gender group and between them etc, either from one or from multiple nations).
Income inequality metrics are used for measuring income inequality, the Gini coefficient being a widely used one. Another type of measurement is the Inequality-adjusted Human Development Index, which is a statistic composite index that takes inequality into account. Important concepts of equality include equity, equality of outcome, and equality of opportunity.