They are different. A component pouch is specialized equipment.
tl;dr The rules specifically require a component pouch which is a listed peice of equipment different from a pouch.
Rules specifically require a component pouch
The material component aspect of casting a spell specifically calls out the use of an arcane focus or component pouch.
Component pouch covers the cost of mundane components and does not require the caster to retrieve components from around their person (that might require use an object) while casting it.
Component pouch and pouch are different pieces of equipment
In the basic rules adventuring equipment, a pouch is 5sp while a component pouch is 25 gp. The component pouch takes the place of an arcane focus for a single classed spellcaster as elaborated on in the answer here.
The regular pouch does not take the place of the arcane focus, nor does it supply the mundane (no specifically cost listed) components of spells.
Can still cast message without the pouch.
Since the character directly owns the components, they can still cast the message spell. A component pouch or focus can be used in place of mundane components.
A character can use a component pouch or a spellcasting focus (found in “Equipment”) in place of the components specified for a spell.
Copper wire not consumed
The message spell does not state that the component of the spell is consumed, so a single short piece of wire should be sufficient for as many castings as you like.