Substantially identical funds: Index funds offered by different fund companies but tracking the same index are substantially identical (Vanguard 500 Index ETF (VOO), Schwab S&P 500 Index Mutual Fund (SWPPX)).
Different funds: Index funds managed by different fund companies, tracking different indexes and exhibiting low overlap in their holdings are not substantially identical (Fidelity Total International Index Mutual Fund (FTIHX) tracking MSCI All Country World ex US IMI Index vs. Vanguard Total World Stock Index Mutual Fund (VTWAX) tracking FTSE Global All Cap Index).
Similar funds: Funds offered by the same fund company with different management approaches and investment styles but significant holdings overlap are likely considered not substantially identical (Schwab S&P 500 Index Mutual Fund (SWPPX): passive large-cap blend fund tracking S&P 500 Index, Schwab Large-Cap Growth Mutual Fund (SWLSX): active large-cap growth fund benchmarked against Russel 1000 Growth Index).