What is quantitative trading ?
I invite you to refer to investopedia definition – this site is a wikipedia for finance & trading-
Quantitative trading consists of trading strategies based on quantitative analysis, which rely on mathematical computations and number crunching to identify trading opportunities. Price and volume are two of the more common data inputs used in quantitative analysis as the main inputs to mathematical models.
What is algorithmic trading ?
Keep the reference to investopedia definition :
Algorithmic trading is a type of trading that uses powerful computers to run complex mathematical formulas for trading. An algorithm is a set of directions for solving a problem. An example of an algorithm is an algebraic equation, combined with the formal rules of algebra. With these two elements, a computer can derive the answer to that equation every time.