I think you are asking about actively managed funds vs. indexes and possibly also vs. diversified funds like target date funds. This is also related to the question of mutual fund vs. ETF.
First, a fund can be either actively managed or it can attempt to track an index. An actively managed fund has a fund manager who tries to find the best stocks to invest in within some constraints, like "this fund invests in large cap US companies". An index fund tries to match as closely as possible the performance of an index like the S&P 500.
A fund may also try to offer a portfolio that is suitable for someone to put their entire account into. For example, a target date fund is a fund that may invest in a mix of stocks, bonds and foreign stock in a proportion that would be appropriate to someone expecting to retire in a certain year. These are not what people tend to think of as the canonical examples of mutual funds, even though they share the same legal structure and investment mechanisms.
Secondly, a fund can either be a traditional mutual fund or it can be an exchange traded fund (ETF). To invest in a traditional mutual fund, you send money to the fund, and they give you a number of shares equal to what that money would have bought of the net asset value (NAV) of the fund at the end of trading on the day they receive your deposit, possibly minus a sales charge. To invest in an ETF, you buy shares of the ETF on the stock market like any other stock. Under the covers, an ETF does have something similar to the mechanism of depositing money to get shares, but only big traders can use that, and it's not used for investing, but only for people who are making a market in the stock (if lots of people are buying VTI, Big Dealer Co will get 100,000 shares from Vanguard so that they can sell them on the market the next day).
Historically and traditionally, ETFs are associated with an indexing strategy, while if not specifically mentioned, people assume that traditional mutual funds are actively managed. Many ETFs, notably all the Vanguard ETFs, are actually just a different way to hold the same underlying fund.
The best way to understand this is to read the prospectus for a mutual fund and an ETF. It's all there in reasonably plain English.