I am trying to find Vanguards S&P 500 index funds and Vanguards Dow index funds. But I only see "Mutual" or "ETFs" Funds. Is Vanguard Mutual funds equivalent to a index fund?
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.
You cannot actually buy an index in the true sense of the word. An index is created and maintained by a company like Standard and Poor's who licenses the use of the index to firms like Vanguard. The S&P 500 is an example of an index. The S&P 500 "index includes 500 leading companies", many finical companies sell products which track to this index. The two most popular products which track to indexes are Mutual Funds (as called Index Funds and Index Mutual Funds) and Exchange Traded Funds (as called ETFs). Each Index Mutual Fund or ETF has an index which it tracks against, meaning they hold securities which make up a sample of the index (some indexes like bond indexes are very hard to hold everything that makes them up).
Looking at the Vanguard S&P 500 Index Mutual Fund (ticker VFINX) we see that it tracks against the S&P 500 index. Looking at its holdings we see the 500-ish stocks that it holds along with a small amount of bonds and cash to handle cash flow for people buying and sell shares. If we look at the Vanguard S&P 500 ETF (ticker VOO) we see that it also tracks against the S&P 500 index. Looking at its holdings we see they are very similar to the similar Index Mutual Fund.
Other companies like T. Rowe Price have similar offering. Look at the T. Rowe Price Equity Index 500 Fund (ticker PREIX) its holdings in stocks are the same as the similar Vanguard fund and like the Vanguard fund it also holds a small amount of bonds and cash to handle cash flow.
The only real difference between different products which track against the same index is in the expense ratio (fees for managing the fund) and in the small differences in the execution of the funds. For the most part execution of the funds do not really matter to most people (it has a very small effect), what matters is the expense (the fees paid to own the fund). If we just compare the expense ratio of the Vanguard and T. Rowe Price funds we see (as of 27 Feb 2016) Vanguard has an expense ratio of 0.17% for it Index Mutual Fund and 0.05% for its ETF, while T. Rowe Price has an expense ratio of 0.27%. These are just the fees for the funds themselves, there are also account maintenance fees (which normally go down as the amount of money you have invested at a firm go up) and in the case of ETFs execution cost (cost to trade the shares along with the difference between the bid and ask on the shares).
If you are just starting out I would say going with the Index Mutual Fund would easier and most likely would cost less over-all if you are buying a small amount of shares every month. When choosing a company look at the expense ratio on the funds and the account maintenance fees (along with the account minimals). Vanguard is well known for having low fees and they in fact were the first to offer Index Mutual Funds.
For more info on the S&P 500 index see also this Investopedia entry on the S&P 500 index.
Do not worry if this is all a bit confusing it is to most people (myself included) at first.