No, some of Vanguard's funds are index funds like their Total Stock Market Index and 500 Index. In contrast, there are funds like Vanguard PRIMECAP and Vanguard Wellington that are actively managed. There are index funds in both open-end and exchange-traded formats. VTI is the ticker for Vanguard's Total Stock Market ETF while VTSMX is an open-end mutual fund format.
VOO would be the S & P 500 ETF ticker while VFINX is one of the open-end mutual fund tickers, where VIIIX has a really low expense ratio but a pretty stiff minimum to my mind.
As a general note, open-end mutual funds will generally have a 5 letter ticker ending in X while an ETF will generally be shorter at 3 or 4 letters in length.