Horizontal and Vertical Equity
When looking at tax "fairness", we typically look at two different goals in distributions to look at equity; vertical and horizontal equity.
This principle claims that there is "equal treatment of equals." In other words, individuals who have the same wealth, or are in the same income bracket, should face the same tax rate.
This principle claims that wealthier people, or those with access to more resources, should pay higher taxes.
Taxes are classified as being Progressive, Proportional, or Regressive. These designations focus on the relationship between tax rates and income simply because all taxes, regardless of whether they are levied on income or on a product or building or parcel of land are ultimately paid out of someone's income.
A tax is progressive if its average rate increases as income increases. Such a tax claim not only a larger absolute amount, but also a larger fraction or percentage of income as income increases. Now say the rate structure is such that the household with an annual taxable income of less than $10,000 pays 5% in income taxes, the household realizing an income of $10,000 to $20,000 pays 10%, $20,000 to $30,000 pay 15%, and so forth. This would be a progressive income tax.
A regressive tax is one whose average rate declines as income increases. Such a tax takes a smaller and smaller proportion of income as income increases. A regressive tax may or may not take a larger absolute amount of income as income expands. in this case, you pay 15% if you earn less than $10,000; 10% if you earn $10,000 to $20,000; 5% if you earn $20,000 to $30,000 and so on. This is a regressive income tax.
A tax is proportional when its average rate remains the same, regardless of the size of income. Suppose tax rates are such that a household pays 10% of its income in taxes, regardless of the size of its income. This would be a Progressive Tax.