Defense starts from the Strikers
Think of this concept like this, if you start to tactically press on opponent half, you have to run less to cover on your own half and at the same time you get the ball when opponent is not prepared and most vulnerable.
Your fullbacks and midfield will run actually same or less, because they don't have to run back, but they are already in position forward to press.
Gurdiola and Jurgen Klop made this style very popular, efficient and most successful on world stage dominating other teams in the past and currently.
Albeit Gurdiola is more famous because of his team possession game, he also incorporated this a lot with teams that can run.
While Klop's Borussia Dortumnd and now Liverpool are teams that are know for breaking down space and tactically high press in means to run to defend less and get in good position when opponent is not prepared, basically forcing errors. His method works very well even against best teams like Barcelona at the time and now Man City.
Still Klop's teams are also very good with their technique skills to keep the possession, which is in turn also never mentioned.
In the end many times over Klop's teams, Borussia Dortumnd Liverpool proved that they work quite well aand even better against Guardiola teams which focus mostly on possession.
Since the only good counter attack to high press is wide ball possession, long passes or long balls over defenders.
But with High Passes you risk losing possession, especially if you lack tall players, so your options are really limited to long passes in open space, which Klop teams are fully aware off and crush that space.
Which in turns results in the team that is high pressing running less after the ball and long pin point accurate passes can only be made by top players, not all of them.
With wide ball possession defenders are spread about which makes the gaps bigger for attacker if the pressuring team gets the ball, which in turns put pressure on defending team and make they hesistant.
Even more prone to that if they make mistake or have lost to high press before.