I would send out seperate thank you notes. Most people attending a shower will also attend a wedding and give gifts for both.
I don't know why, but for some reason the gift-opening at both my showers was the most awkward, uncomfortable thing in the world for me!! I was just handed a ton of presents, you'd think I'd be like a kid on Xmas right?? I was so shy...which for me is doubly hilarious :)
I would look at the card first and announce who the gift was from, then open it and thank the person who gave it to me in kind of a general way since I was sitting up in front of everyone. And then I wrote individual, more personal thank-yous after.