Yep, omegamaulers, your in the right forum. Same rodeo, same bull, new rider ....
Tri-ply and Multi-Ply are used to describe two totally different products - but both totally legit in the description.
With All-Clad tri-ply - you have a sandwich of 3 metals such as stainless steel or copper outside, aluminum center layer , and stainless steel inside (tri ply) ... the aluminum core comes all the way up the sides of the pans and the bottom and sides of the pans are the same thickness. Brands that use this construction tend to be the more expensive.
The other "tri-ply" are only triple layers on the bottom of the pot ... these are easily spotted because they have a thick encapsulated disk on the bottom - the bottom has a significantly thicker base than the sides .... the tri-ply is only on the bottom - and the sides are just single layer of stainless steel. This is a cheaper form of construction and thus is less expensive. There are several brands of "tri-ply ... multi-ply" that use this form of construction such as Emerilware, Wolfgang Puck's Bistro Collection, Martha Stewart, Cooks Essentials, etc. I've talked to people who have the Sam's Club cookware and they love it.
IMHO - learning how to use your cookware will do more for your cooking than how much you pay for it. But, as GB said, I would also suggest suggest getting something with a little heft and metal handles that are rivited on ... handles that are welded or screwed on don't last as long and plastic handles won't let you put the pan in the oven to finish cooking the sidh.