Strength Training Teminology PSA: there is a difference between Lateral Squats and Lateral Lunges
A Lateral Squat is stationary, meaning the feet never leave the ground, as you can see in the first video.
A Lateral Lunge, which is a progression from the Lateral Squat for us because of the increased deceleration, is more dynamic as the feet are now moving from side to side instead of staying on the ground, as you can see in the second video.
Think Split Squat vs. Lunge.
Hope that helps!