Mutual funds deal with buying and selling by themselves, off the stock market. You must deal with the actual fund, in order to purchase shares. With an ETF (Exchange Traded Fund), anyone can buy the ETF on the open market - it's just sitting there, with a ticker symbol, like any other company.
I'll give you a concrete example - someone has a Fidelity account, and wants to buy either a Vanguard mutual fund (VTSAX) or a Vanguard ETF (VTI). When they try to "transaction Fee non-Fidelity funds" like VTSAX, the cost is $49.95, which is probably shocking, so here's the link:
https://www.fidelity.com/trading/commissions-margin-ratesWhat happens if you buy the ETF version, instead? VTI trades on the open market. If you check that same link, above, you'll see "ETFs ... All online ETF trades" costs $0. Fidelity is already linked to the stock exchange - but they have to make a special effort to do a mutual fund transaction with Vanguard. That's why they charge more, and it's a good example of how an ETF differs from a mutual fund.
If you buy VTSAX at Vanguard, it's $0. Vanguard is setup to handle it's own mutual funds. At Fidelity, you can buy Fidelity mutual funds for $0. But once you buy mutual funds of another company, it can be expensive.