Yes, they are different brand names, so different manufacturers. In terms of effectiveness, as you found out, nope. However, I LOVE my Vivelle [which is the US version of Estradot, they're both by Novartis] because it's tiny and sticks a lot better, so you're in luck - the cheaper one is also better to use, IMO.
I've heard a lot of people say Climara has some trouble sticking, and it's b/c the adhesive is actually the delivery method for the estrogen; seems like Novartis cracked the secret of how to make that adhesive also *sticky* better than Bayer [Climara]. I've never had trouble with Vivelle sticking, though it does bunch up a tiny bit, and they've also been a heck of a lot more comfortable to wear. I was on the generic Climara for the first few months and those were terrible - huge and awkward and fell off constantly and gave me bad skin irritation.
