I think there are two different issue here.
First, use stochastic vol or garch to fit or predict vol, this is normally used in statistical arbitrage trade, where you correlate the market dynamic with your model parameters.
Second, long/short volatility strategies. This is based on your view of the implied vol or implied vol against realized vol. Regarding to the difference between the covered call and the straddle, I think for the previous one you need to continuously rebalance your stock position to make it delta neutral, in which situation you will bear the risk from the gamma weighted realized vol and BS vol difference. For the straddle, I don't think you need to make it delta neutral. There are conparisons between the three strategies. It is is hard to tell which strategy is definitely better than the others.
Third, it is also popular to trade the vol of vols and dispersions.