What is the difference between a Mutual fund and an Annuity?

They are totally different things. A mutual fund is collection of investments such as stocks or bonds using the pooled money of a many investors, each of whom own a number of shares of the fund based on their investment. Mutual funds may be "closed ended" - meaning the investments are planned to be sold off and the cash returned to the investors at that time - or open-ended, where the fund may run for as long as they want. In either case mutual fund shares may be bought and sold on exchanges just like stock shares.

An annuity is "reverse life insurance" - in exchange for an up-front fee the annuity company agrees to pay you a certain amount of money every month as long as you live.