High Frequency Trading should have been called Low Latency Trading.
1) How algorithmic is it? How much of the trading decision is made by a computer and how much human intervention is there.
2) How often does it trade? Some electronic trading systems can trade thousands and thousands of times a day, while others only trade a few times a quarter.
3) How long does it hold a position and/or leave a quote on the market? Some trading systems are designed to never hold positions and others hold positions constantly.
4) What latency requirements does the trade have from the time the exchange publishes data until the time an order needs to be in the market.
There are electronic trading systems that exist with variables at every end of these spectrums.