If you read Zonal Marking its pretty good at explaining obviously the different tactics of the strongest teams in that "era" of country domination but Barcelona's press is what inspired Klopp (I can't remember if it was Rijkaard's or Guardiola's but I'm sure it was Rijkaard's) but while Barcelona aggressively fought to get the ball back to control the ball again. Klopp's ideas also being inspired by Rangnick's fast transitions. Bundesliga already being heavily counter-attacking Klopp's press is counter-press basically its countering the counter attack exploiting the transition from defence to attack. The entire chapter though on Guardiola trying to adapt to the Bundesliga and every team being counter-attacking is awesome.
Liverpool's main thing is that its fullbacks are its playmakers (unlike say a number 10) Liverpool especially use a cross-field ball but unlike most teams doing it say fullback to midfielder or attacker its fullback to fullback (as seen in Salah's goal)
Its why United had a better game because they basically man marked the fullbacks which is crazy to think about.