Traditional investments refers to investments in publicly traded individual stocks, ETFs, mutual funds, bonds or just cash and money market funds.
Alternative Investments refers to types of investments outside the spectrum of publicly traded stocks, bonds and mutual funds.
Alternative investments are sometimes referred to as just "alts" or "alternatives".
Private Markets refers to a subset of alternative investments focused on non publicly traded strategies.
All private markets are alternative investments, but not all alternative investments are private markets.