No, HDFC Securities doesn't offer direct mutual funds. The company only offers regular mutual funds.
Direct mutual funds are sold directly by AMC or fund houses. Regular mutual funds are sold through distributors and agents who in return get paid a commission of 1 to 2%. The commission paid by the AMC to the agent is charged to the customer indirectly through MF management fees.
The commission paid every year becomes a substantial amount if you stay invested for a longer-term. In direct mutual funds, you save on this commission amount and get higher returns.
Zerodha and 5paisa are 2 stock brokers who offer direct mutual funds.