Roth IRA
Contributions are made with after-tax assets, all transactions within the IRA have no tax impact, and withdrawals are usually tax-free. Named for Senator William Roth.
Traditional IRA
Contributions are often tax-deductible (often simplified as "money is deposited before tax" or "contributions are made with pre-tax assets"), all transactions and earnings within the IRA have no tax impact, and withdrawals at retirement are taxed as income (except for those portions of the withdrawal corresponding to contributions that were not deducted).
SEP IRA (Simple Employee Pension)
A provision that allows an employer (typically a small business or self-employed individual) to make retirement plan contributions into a Traditional IRA established in the employee's name, instead of to a pension fund account in the company's name.
Simple IRA
A simplified employee pension plan that allows both employer and employee contributions, similar to a 401(k) plan, but with lower contribution limits and simpler (and thus less costly) administration. Although it is termed an IRA, it is treated separately.