Funds are just collections of underlying securities. Managers of funds are typically paid a fee to pay for the operating expenses of the fund and to generate a profit for the management firm.
Exchange Traded Funds (ETFs) are funds that track market indices in order to mirror the return of a given asset class or basket of underlying securities. They are traded on exchanges in the same way that a stock or bond would be traded, making them more liquid and tax-efficient than mutual funds.
Examples of ETFs include whole market tracking funds, S&P500 funds, and funds that track other major asset classes. ETFs may also be used for thematic investing (e.g., tracking tech stocks or socially responsible indices), factor investing (e.g., volatility or any other attribute of collections of securities), providing leverage, or tracking a variety of other assets in a liquid way (e.g., gold, foreign bonds, bitcoin).
Mutual funds are collections of securities that are valued and redeemable daily. A mutual fund investor buys shares of a fund that pools investor money and then a manager directly invests that money according to the investment thesis of the fund.
Many mutual funds are active rather than passive, empowering managers with leeway to attempt to beat the market benchmark their fund tracks.
There are other types of funds that are often not traded on exchanges. These include real estate investment trusts (REITs) that invest in commercial or residential real estate, private equity funds that invest in companies that are not publicly traded, venture capital funds that invest in smaller and higher risk private companies, hedge funds that invest in both public and private securities, and others.