HIIT = high intensity interval training. Basically, you sprint as fast as you can, then take a recovery period. The intense part lasts only 30-60 seconds, and you can't do much more than 20 minutes (excluding warm-up and cool-down), because the intensity is at your limit.
Interval training. Fast, slow, fast, slow as you are doing. The interval can be 1 minute each to 10-15 minutes each. You can keep up the intervals for much longer, because they are not necessarily at your limit. Or you can use incline intervals.
Fartlek = a Swedish method. Basically, you mix up moderate, fast, sprint, incline, at random, not really following a set interval. The times of the intervals can vary during the session. I have tried this when I am just too tired or bored to do my usual routine on the treadmill. Although the randomness is not a surprise when you are setting the changes yourself, it is a nice break, and you get all levels of work within one session.
Hope this helps, and good luck in progressing with your speed.
Do or don't do; there is no try (Yoda)