What is the difference between HFT and quantitative trading?

HFT and quantitative trading is basically the same thing.  Both use algorithms for every investment and trading decision.

HFT is trying to find small inefficiencies in how real money investors and trader trade. It is fast and speed is an important issue for trading execution.

Quant traders are instead trying to find the holes in how larger institutions trade and find predictable patterns in them instead.

The methods and approaches are very similar for HFT and quantitative trading. The big difference is how long the trades last.