A fixed annuity is a type of insurance contract that promises to pay the buyer a specific, guaranteed interest rate on their contributions to the account for a stated period of time.
A variable annuity is a type of annuity contract, the value of which can vary based on the performance of an underlying portfolio of sub accounts. Sub accounts and mutual funds are conceptually identical, but sub accounts don't have ticker symbols that investors can easily type into a fund tracker for research purposes.
An indexed annuity is a type of annuity contract that pays an interest rate based on the performance of a specified market index, such as the S&P 500.
Indexed annuities are sometimes referred to as equity-indexed or fixed-indexed annuities.