S means somatic. This is a required physical action other than will / words that activates the spell.
M means material. Not all spells make a hardware component disappear – some use sacred symbols that are used again and again. A spell can be considered as a reusable material component.
The simple act of holding a magic wand is not a somatic element, but doing it in a certain way, or grasping it, brandishing it, pointing it, etc., if these are indispensable gestures to launch. the fate, they meet the requirements of the somatic. A spell that paralyzes the wizards but allows them to speak, for example, could allow them to cast verbal spells, but if their wand was to be pointed or shaken to activate it, this paralysis would prevent the activation of those -this.
The fact that some chopsticks are actually magic items does not prevent them from being used as hardware components. Some exotic episodes traditionally required enchanted objects as components.