To add, all SP500 funds are index funds (SP500/SPX is an index).

Mutual funds are typically what you'd be offered if you're investing using a 401k, but in other accounts, you're more likely to find people choosing ETFs. The differences between are a better question for Investopedia. Neither is necessarily better than the other.

All index funds will be passive. Some funds do "pre-load" expected additions to index, but it's not significant. All Vanguard and Fidelity funds will be passive index funds, and only their expense ratios will differ. As dedigans says, only the ER and trading commission matters here because all SP500 index funds are tracking the same thing.