S means somatic. It's a physical action required other than will/words alone that activates the spell.
M means material. Not all spells cause a material component to vanish - some use holy symbols which are used again and again. A wand can be deemed by a spell to be a reusable material component.
Simply holding a wand is not a somatic component, but waving it in a certain way, or picking it up, wielding it, pointing it, etc., if these are required gestures to cast the spell, then they fit the requirements for somatic. A spell that paralyzes wizards but allows them to speak, for example, might allow them to cast verbal spells, but if their wands had to be pointed or waved to activate, that paralysis would prevent those wands from activating.
The fact that some wands are actually magic items does not prevent them from being used as material components. Some exotic spells traditionally required enchanted items as their components.