In the tutorial, they show you, how you can fight on a horse, how you can ride, how you can fight with a shield, how you can block with a two handed weapon, etc...
On the trainings ground, you can only test some weapons.
To be fair, the training ground scene is actually used in the fourth tutorial, you just can't access it in an actual game. But yes, the tutorial is much better than the training ground.
I remember the good 'ol days of a little cold stone room that they locked you in with some psychopathic dude to see who's brains would get bashed out first.