This statement should read, "The unsystematic risk for a specific firm is not similar to the unsystematic risk for other firms in the same industry." Thus, other terms for this risk are firm-specific, or unique, risk.
Systematic risk is not diversifiable. As an investor increases the number of stocks in a portfolio the unsystematic risk will decrease at a decreasing rate. Total risk equals systematic (market) plus unsystematic (firm-specific) risk.