Stochastics are usually applied in the field of derivatives pricing. In this setting the task is to price a derivative such that it fits into the landscape of tradable instruments (no-arbitrage). We work using the risk-neutral measure - usually denoted by $Q$. The measure is derived from other traded instruments.
In risk analysis (e.g. calculate the VaR, ES of this portfolio of stocks or credits) we work in the real world measure $P$. Usually $P$ is in some sense derived from history. This approach is rather statistical.
So the answer is: because this are 2 connected but somehow quite different fields of (quantitative/financial) mathematics.
One important EDIT: The GARCH approach tries to forecast volatility. This is doen by local volatility and stochastic volatility in the world of stochastic analysis/derivatives pricing. Still: GARCH is rather a P-thing (and it is calibrated on the past) and the others are Q-things (calibrated in the market).