Index funds exist as both mutual funds and ETFs; the wrapper changes how you trade them, not what they own. The performance question is narrow: how closely the fund matches the index after costs, measured by tracking-error and by the annual gap attributable to the expense-ratio.
A full-replication fund holds every constituent. A sampling fund holds a representative subset, which is normal for broad bond and small cap indices where holding thousands of illiquid lines is impractical and raises tracking error.
Example: an index returns 11.40% and a fund charging 0.04% returns 11.35%, a 5 basis point gap. A rival charging 0.45% returns 10.93%; over 20 years that 0.41% annual difference compounds to about 8% of ending wealth.
Related: etf, mutual-fund, expense-ratio, tracking-error, index