They really are completely different concepts. In contrast training (Lift it HiiT it - Legs) you do a weight exercise say for 10 reps and then immediately follow the weight exercise with a plyo exercise that is similar to the movement that you just did with a weight. Then you keep repeating this pattern.
The lower body circuit workout doesn't use the concept of contrast training. In HiiT Lower Body Circuit you will do several minutes of lower body cardio exercises before moving on to a weight section that can also last several minutes.
To demonstrate the difference let me show you two videos from the past that are at least similar in concept to what these two videos are like.
Here is a video clip from 2008 STS Plyo Legs ( This workout is similar in concept to Lift it HiiT it - Legs ):
Here is a video clip from 2012 XTrain Cardio Leg Blast ( This workout is similar in concept to HiiT Lower Body Circuit ):
Hope this helps!