How much money people really "make" is open to interpretation, because the amount of money paid out for those people's labor (or for the use of their capital, in the case of investment income) is not necessarily the same amount that winds up in their pockets as spending money. "Disposable" income is what's in your paycheck; discretionary income is what's available after you pay for basic necessities.
All income calculations start with gross income. This is your income before taxes, expenses or anything else. If your job pays you, say, $30 an hour, then your gross income from a 40-hour work week would be $1,200. But anyone who works at a regular job knows that your paycheck — your take-home pay — is usually less than your gross income.
Disposable income is best described as your take-home pay: what's left over after withholding for income taxes and payroll taxes, including Social Security and Medicare. Definitions of disposable income vary around the margins; in some contexts, disposable income is also reduced by pretax deductions for such things as health care and pension plans. In general, though, disposable income is the portion of your income that's "at your disposal," available for you to spend.
Disposable income has to pay for both needs and wants. Some bills you have to pay: housing, utilities and so on. Once you've paid for your basic needs, the remainder is discretionary income — money that you can choose to spend on one thing or another, or that you can save rather than spend. When basic needs eat up all of a family's disposable income, they have no discretionary income, and thus nothing for extras, savings or emergencies.
Wants and Needs
Some people truly have no discretionary income. Others do but don't recognize it because they're spending money on "wants" that they have miscategorized as "needs," or are spending money inefficiently. Everyone needs to eat, for example, but you can choose whether to spend, say, $100 on groceries and make your own meals or spend $250 to eat at restaurants. In the latter case, you're taking $150 worth of discretionary income and choosing to spend it at restaurants rather than on something else.