High frequency trading is a subset of Algorithmic trading.
In simple words, if you have a program that trades it is called algorithmic trading or algo trading. If the algo is designed in such a way that it does a lot of trades it is called high frequency trading.
As you can see in the figure below Algo trading (Co-location, DMA, and Algo) together contribute almost 41% of exchange turnover. The more startling fact is that almost 90% of orders placed on the NSE is through algos(though most orders get cancelled).
So yes, the impact in India is quite high, and because of the lesser retail participation, an event risk is quite high because of the algos.
Automated Trading is the subset of Algorithmic Trading, while HFT is the subset of Automated trading. The below image explains it in a better way:
OMG, 90% of orders! I should start learning AlgoZ atleast.