The techniques are similar.
The difference between the two videos and techniques is in the amount you explode out extending your legs before you try to get your legs underneath your hips in power lifting position.
You can fire out and run your legs under your hips like Marvel did (we can't really see Joe) or you can keep your legs underneath your hips the whole time like Mark did remaining in the power lifting position.
There are advantages to both techniques. The explode out technique has more initial violence and carries focused body weight into an opponent (like diving through a door rather than setting up and punching it). The controlled technique gives you more upward power to redirect and is much more balanced.
Keep in mind in the first truck pushing video they told them it was fourth and goal from the 1, a sustained block is not the goal in that situation.
I prefer the explode out technique more for defense and the controlled technique more for offense. If we both explode out all day we are going to have sore heads.
The big mistake a lot of people make with the first tech is they never try to get their legs back under their hips. They stay extended and push, defender will shuck you after a few seconds (or less) if you do that.