I have a question that seems a bit off topic, but what does qualify as a principle? what does qualify as roots of certain way or ideology/DNA in football?
Those terms are used in very flexible ways during argument.
Is Pep way and Crujif way the same principles? Is Lucho a Barca DNA? Naggelsman? Tuchel? Bielsa?
I use a different methodology. Rigid vs fluid styles, starting with the idea that no system is 100% fluid or 100% rigid, but that there is a predominance and a preference for one over the other in every manager.
Rigid suggests a low tendency to mess with the way players occupy positions, no matter if it's attack, defense, or transitions from one to another. The key of this approach is to have players who are extremely specialized in one position, so-called specialist players. Versatile players aren't as valued as in the fluid styles. The poacher: Inzaghi, Crespo. The destroyer: Gatusso. The creator: Rui Costa, Del Piero. Attackers do the attacking phase, defenders do the defending. You don't see strikers dropping too much to mess with the creation part, you won't see fullbacks as pseudo-midfielders too much, but more as the up and down speed merchants that we know from the past.
This is the stuff BBZ loves. The lower levels of fluidity enhance the individuality of each player, hence why speed, tackling ability, height, muscle, each of these become weapons that allow a player to control his space and the opponents that try to claim it. Imagine Busi alone trying to tackle someone, without Xavi, Pedro, Alves pressing that guy from all angles. It would be extremely bad and counterproductive. You'd want a Makelele or a Casemiro for that 10 times out of 10. Someone who could put a firm leg to block the action, someone who could hang around in physical duels, someone to make a cynical tactical foul, etc.
Normally, rigid managers want players to do what they are known to do best, without trying to be too clever. In this case, someone like Gatusso becomes more of an asset in a defensive position than a technical, all-around better player like Busquets, simply because of his more specialized nature.
Fluid is the opposite. Managers found out that it's potentially more beneficial for players to move around. That you can move and alter positions frequently and still make sure you control the areas that matter the most to you.
The fluid system needs players who are very adaptable and are very comfortable playing a multitude of positions. Sometimes, inside only 5 mins, when a pressing trap fails, and the team is playing aggressively, chasing the ball, you can find yourself having to defend a position or block an opponent who is not in your area, simply because that's how the game developed. Fluid systems assume that any player almost can perform the roles required from them. Hence why we start to see more blurred roles, like False 9, with players like Firmino (now Jota), Mertens, Messi, playing the type of role which has them moving around without staying too long in a static position.
Fluid systems dislike overly individualistic players because in fluid systems there is almost no distinction between attack and defense. Every player has a role in both. This is why for example Xavi hates Pogba's profile. He is not a player that has the IQ, the discipline, and the selflessness to do what is required of him in different aspects of the game if the game asks for it. He will always approach the game with the mindset of: "I'm a star. My job is to create, your job is to defend if I lose the ball". No coincidence he played his best football in a rigid team like Juventus under Allegri. This is the main reason why Pep and Klopp are both hesitant to work with superstar personalities, btw. Salah, Mane, these guys are like Pedro and Villa. Not like Neymar. Not like Ronaldinho. Their style is built on the idea that every player will be able to perform multiple roles, which requires a certain mindset, call it humbleness. Players like Neymar and Pogba are too aware of their talent and thus consider that it's somewhat beneath them to do defensive work.
BBZ calls them schoolboys. In reality, they are players who have less star-like attributes but, instead, have better professionalism, work harder, and often show a higher tactical understanding of the game. They can play multiple positions, they respect the plan of the manager, and so on.
Some names now.
Fluid team: Pep, Klopp, Flick, Naggelsmann, Ten Hag, Bielsa, Tuchel, Luis Enrique etc.
Rigid team: Nearly all Italian greats (Lippi, Capello etc.), Simeone, Mourinho, Zidane, Max Allegri, Pochettino, Conte.
Of course, there are also levels and levels. Some share characteristics from both areas (like Tuchel, Pochettino for example). I'd say currently the extremes are Guardiola for the fluid team vs Simeone for the rigid team.