Magical Foci and Casting

Conjurer and White Magic requires "A wand or cane made from unworked wood", Thaumaturgy and Black Mage requires a "scepter or staff, within which is housed a medium—a natural stone imbued with magical properties". How is it then that Ystola and Graha'Tia can cast magic from both schools using only one type of staff? How do some characters cast magic without any apparent weapon -- can high level mages simply forgo their foci and cast with their hands?