... are all the same thing right?

Eg. Yesterday at the gym did half hour on crosstrainer, five min warm up on treadmill then what (I?) consider intervals - 2 mins walk at 6km/h then 1.5 mins run at 11km/h... and so on and so forth 2 mins followed by 1.5 mins slow quick slow quick for 35 mins followed by five min cool down.

Is this 'right'? Any tips on ways to change/tweak it if not?

(NB. For info I'm hoping to be able to work up to doing more of a jog pace not walk in the 'slow' period and increase the speed for the running sections)

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.