A mutual fund has several classes of shares that are charged different fees. Some shares are sold through brokers and carry a sales charge (called load) that compensates the broker in lieu of a fee that the broker would charge the client for the service. Vanguard does not have sales charge on its funds and you don't need to go through a broker to buy its shares; you can buy directly from them. Admiral shares of Vanguard funds are charged lower annual expenses than regular shares (yes, all mutual funds charge expenses for fund adninistration that reduce the return that you get, and Vanguard has some of the lowest expense ratios) but Admiral shares are available only for large investments, typically $50K or so. If you have invested in a Vanguard mutual fund, your shares can be set to automatically convert to Admiral shares when the investment reaches the right level.
A mutual fund manager can buy and sell stocks to achieve the objectives of the fund, so what stockes you are invested in as a share holder in a mutual fund will typically be unknown to you on a day-to-day basis. On the other hand, Exchange-traded funds (ETFs) are fixed baskets of stocks, and you can buy shares in the ETF. These shares
are bought and sold through a broker (so you pay a transaction fee each time) but
expenses are lower since there is no manager to buy and sell stocks: the basket is fixed.
Many ETFs follow specific market indexes (e.g. S&P 500). Another difference between
ETFs and mutual funds is that you can buy and sell ETFs at any time of the day just
as if you could if you held stocks. With mutual funds, any buy and sell requests
made during the day are processed at the end of the day and the value of the shares
that you buy or sell is determined by the closing price of the stocks held by the mutual
fund. With ETFs, you are getting the intra-day price at the time the buy or
sell order is executed by your broker.