What used to be simple wands in 2nd edition are mostly rods now. So no, Elminster's power isn't coming from a wand, it's coming from a rod. It's esthetic choice because we're used to pointy sticks rather than metal ones. This is because there was an overhaul in the magic system between editions.
Here are the 3.5 definitions of a wand and a rod:
Definition of a wand: A wand is a thin baton that contains a single spell of 4th level or lower. Each wand has 50 charges when created, and each charge expended allows the user to use the wand’s spell one time. A wand that runs out of charges is just a stick.
A typical wand is 6 inches to 12 inches long and about ¼ inch thick, and often weighs no more than 1 ounce. Most wands are wood, but some are bone. A rare few are metal, glass, or even ceramic, but these are quite exotic. Occasionally, a wand has a gem or some device at its tip, and most are decorated with carvings or runes. A typical wand has AC 7, 5 hit points, hardness 5, and a break DC of 16.
Definition of a rod: Rods are scepter-like devices that have unique magical powers and do not usually have charges. Anyone can use a rod. Rods weigh approximately 5 pounds. They range from 2 feet to 3 feet long and are usually made of iron or some other metal. (Many, as noted in their descriptions, can function as light maces or clubs due to their sturdy construction.) These sturdy items have AC 9, 10 hit points, hardness 10, and a break DC of 27.
This is why the previous edition wand of wonder became a rod of wonder in 3rd edition. Elminster's "wand" is a rod if you want it to cast higher level spells or contain several different spells.