Wand/Rod of Fire Bolts does how much damage? More for mages?

[danbang]

How much damage is done by, say, a Wand of (let's say) Fire Bolts? Is it the same as a Rod of Fire Bolts? A Staff (if there is such a thing)?

I had sort of assumed it would be the same as if I, as a mage, cast the same spell, so I could look up the damage by Browsing my magic books. Then I realized that, not only does my damage increase as I gain more character levels, but some characters aren't even mages -- by that yardstick, a non-spellcaster would do no damage when using a wand, which is ridiculous.

What about Frost Bolts, instead of Fire Bolts? What about Lightning Bolts vs Lightning Balls? etc. etc. Would love to know.

If it's too much of a spoiler, then at least tell me: does damage from a wand/rod increase as my character level increases? In other words, as my own Fire Bolt (say) spell gains more damage with a rise in my character level, are my offensive magic items worth less because they stay at the same damage even as I descend the dungeon levels to face fiercer monsters?

Thanks for any !Wisdom or =Wisdom or "Wisdom you can send my way.