Exactly. They are just completely different skillsets. Being a great football player doesn't necessarily mean you become a great football manager. It requires a whole different level of patience and a different type of discipline to that of a player (and you need a lot of discipline to becone a great player and remain that way).
As a player you just need to make sure you are committed to your craft, how you fit and contribute to the team and your own responsibilities mainly. As a coach you need to see the bigger picture, how everything fits in with each other and you need to be able to clearly articulate that to the team in a way that gets the best out of them without being frustrated that they can't do what you were able to do as a player.
It's like being a great employee who knows everything technically about to do his job better than most other people. Those same people don't necessarily become great managing a team doing the exact same thing they did just because they were great at that particular role. It happens, but it's not a given.
Now Fabregas, yeah, I don't like him, so I'm biased against him. Sue me.