First, let's define a mutual fund. When you invest in a mutual fund, the fund itself is invested in multiple investments. The mutual fund allows you to make diversified investments in an easy way. For more information, see What is a mutual fund?
Now that we know what a mutual fund is, let's talk about stock mutual funds. Mutual funds can invest in any number of different investments (bonds, precious metals, short-term debt), but stock mutual funds are mutual funds that invest primarily in stocks. Stocks are probably the most common investment for mutual funds, so often when you hear about mutual funds, it is assumed that it is investing in stocks.
The managers of a fund decide what specific investments a mutual fund will make. Mutual fund management can be split into two broad categories: Actively-managed and passively-managed. In an actively managed fund, the managers take an active role in researching potential stocks and continuously making buy and sell decisions for the fund. In a passively-managed fund, the fund invests in a fixed list of stocks, and rarely buys or sells new stocks. Passively-managed funds have several advantages over actively-managed funds, including lower fees and less stock turnover, resulting in tax advantages. The list of stocks that passively-managed funds invest in is usually the same as a stock index or group of indexes, so another name for passively-managed funds is index funds.
Exchange-traded funds (ETF) are special types of mutual funds that are traded on the stock exchange like a stock. With traditional mutual funds, you generally send your investment money directly to the mutual fund manager, but with an ETF you invest in the fund by buying shares of the ETF from your stock broker in the same way that you would purchase shares of an individual stock. ETFs can be either actively-managed or passively-managed (index funds), but the majority of ETFs are stock index mutual funds, so sometimes you will see people discuss ETFs and assume that they are index funds. For more information, see What are the important differences between mutual funds and Exchange Traded Funds (ETFs)?