The first wave was replication. Index funds copied the U.S. stock market, European stock markets, the investment-grade bond market, and so forth. Those were the early entrants, and they became the dominant entrants. Currently, the vast majority of indexed assets are with market replicators. For most investors, such funds are synonymous with the term "indexing."
The second wave brought tilting. In 1981, Dimensional Fund Advisors decided that if small-value stocks would outgain other stocks, as its research suggested, then perhaps funds should limit themselves to the small-value segment. The company created indexes to match its beliefs, and then funds for those indexes. The practice of factor indexing--that is, indexing by restricting the portfolio to securities that are exposed to one or more investment "factors"--had begun.