Quantitative trading is the use of mathematical models to determine when and how to trade. Algorithmic trading uses mathematical models in conjunction with computer code to perform the same function.

Quantitative trading might consist of gathering data over a long period of time, calculating correlations between stocks, and determining historical performance. Algorithmic trading might consist of algorithms reacting to every tick in the market - either making or losing money based on whether it was advantageous or not to make that particular trade.

Quantitative trading is a type of technical trading that seeks to profit by exploiting patterns in the price movement of forex, stocks, commodities, currencies, or other assets.
Algorithmic trading is also a type of technical trading that seeks to profit by exploiting patterns in the price movement of stocks, commodities, currencies, or other assets. Both quantitative and algorithmic traders use computers to identify opportunities for trading.