Wand of Spell Storing? Never really heard of such a thing.
Wands are generally spell trigger items holding a particular spell, and allowing it to be used at the wand's caster level 50 times. (i.e. it's a charges item).
Could someone create a Spell Storing item in the form of a carved piece of wood or bone? Yeah, probably, but it would follow the rules for spell storing items (i.e. rings) and cost a lot more, since the "wand" form is effectively slotless.
Now, to the exact question: Spell storing items don't cast any spell that wasn't put into them, and can be used by any class. Even a non-caster can use spells in a Ring of Spell Storing.
The Ring casts the spell at the minimum caster level needed for the spell. For example, a 15th level Wiz' puts a Fireball in the ring, it casts as a 5th level caster (minimum needed to cast the 3rd level spell).
A weapon with the Spell Storing property casts it at the same level as the caster who put it in, but is limited in other ways:
1) The spells it can store are limited to targeted* spells, so no Fireballs.
2) The spell or spells discharge, at the wielder's discretion, when they score a hit with that weapon. That is, if the weapon holds several spells they either all go off or none of them do, based on whether the wielder chooses and whether they hit.
On a more general base, an actual Wand (i.e. the spell trigger item with charges) can be used by anyone who has that spell on their class spell list, even if they themselves can't cast it. As an example, a Sorcerer may or may not have Fireball as one of the spells they can cast, but they could still use a Wand of Fireballs. A Wand of Cure Light Wounds could be used by a Druid or Cleric, of course, but also by a Ranger or Paladin even if they were 1st level and didn't have any spells yet.
So it's not necessarily tied to the class of the Wand's creator so much as it is to the classes that can use that spell
*"Targeted" spells are a specific type of spell. In the spell descriptor block of any given spell it will include "Area", "Effect" or "Target". One and only one of those will apply. Targeted spells are those that specify a Target, rather than an area or an effect. For example, Alter Self has "Target: You", while "Color Spray" specifies "Area: 15 ft cone". Summon Monster has an Effect descriptor, since it doesn't directly affect any creature, nor does it cover any specific kind of area.
Hope this helps.