In "All about High Frequency Trading", by Michael Durbin, he seems to imply that HF and algo trading are completely different and that HF is more about arbitrage/market-making whereas algo trading is about stat arb.
Executions for all trades should be fast regardless if it's algo or HF. An algo that doesn't trade often is not HF. But HF could mean different things to different people. Rather than guess, ask them what their definition of it is in the interview. But none of that makes much difference. Just get yourself across as an intelligent and pleasant kind of guy will more often get you the job than not.
Good post by Joe.
If they want the code to run fast they are not talking about latency. Your code should be optimized for speed on the particular server you are using. In the highest sense that would mean processor specific assembly code. But as Joe said ask them exactly what they want. If they are interested in you they will be happy to explain it to you.