The floating island Samiel was on the 5th Floor of the Tower.
While Yvraine was training with the Lord Moon Sword Elraroth Daeric Yaennernamis, Samiel was doing his own training, which was vastly different from her. While Yvriane was focusing on mastering her sword style, Samiel was learning Mana Control Method.
Mana Control Method was basically a technique to control Mana. Not everyone was using the Mana Control Method, typically for people in the Lower Worlds didn't really have a Mana Control Method or only Nobles had it. Also, based on the strength of the World, then also the Mana Control Methods would differ and in the end, the Mana Control Method and its grade was something akin to a separation line between users of Mana.
It didn't really matter if they were Casters, Combatants, Warriors, Priests or Mages; everyone used the Mana in one way or another, and without a proper Mana Control Method, one's combat prowess would be countless times lesser compared to those who had it.