Above is a video I created that highlights, in my opinion, some of the key aspects of a "Mid-Level Press" or "Medium Defensive Block".
To summarize, these aspects include:
1.) Establishing a purposeful Line of Confrontation in the Midfield Third
2.) Collective shape must be compact vertically
3.) Collective shape must be compact horizontally
4.) Must force opposition into predictable passes and anticipate those passes for effective pressing
5.) Individuals must understand when to hold their positioning within their shape vs. leaving their position to press the ball (hold vs. press)
Two examples of teams and coaches that I believe execute this style of defense at a high-level are: Atletico Madrid (under Diego Simeone) and Manchester United (under Jose Mourinho).
Feel free to share opinions and observations.