Magical wands need to be held to cast their spells.

Does holding the wand count as a material component for the wand's spell?

And if a command word needs to be used, is it considered a verbal component for the spell?

This matters for features such as Subtle Spell, Archdruid, or to identify a spell to Counterspell.

Casting a spell from a wand requires no components

Some magic items allow the user to cast a spell from the item, often by expending charges from it. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. (DMG Chapter 7 "Activating an Item")

Wands are magic items and that means that no components are required for spells cast from them unless the wand's description says it does (and I don't know of any that do).

If a command word or action is needed to activate the magic item, that is a separate thing from spell components completely.

Activating some magic items requires a user to do something in particular, such as holding the item and uttering a command word, reading the item if it is a scroll, or drinking it if it is a potion. (DMG Chapter 7 "Activating an Item")

Activating a magic item must happen before the spell within it is activated. And if the spell explicitly requires components, those will be required in addition to any activation requirements.

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.