Skillet Cooked Shrimp Texture

I was always taught to take the head and tail between your fingers of each hand, pull it out straight, push together slightly, then pull apart. That should pull the whole carapace back off the body. Then you can pull off the head (and legs if they're still there) and you're done.

However, I've seldom gotten it to work when raw, and less so when cooked.

I agree, cooked shrimp are harder to peel, and just add an unwanted challenge to the diner when included in most dishes.

According to this study, frozen seafood has a density ranging from 972 to 1017 kg/m³. Thawed, raw seafood at 20°C has a density ranging from 1042 to 1093 kg/m³. Since the density of water at room temperature is about 998 kg/m³, it is certainly possible—and most likely normal—for one batch of frozen seafood to float while another sinks. Thawed seafood that has been brought to room temperature, on the other hand, should almost always sink since its minimum density (1042 kg/m³) is higher than water's. Therefore, I would only worry if the shrimp continue to float after they have been thawed. If they are shell-on, there is a chance that there could be air stuck between the shell and the body, though, which would of course be perfectly fine yet affect the density/floating.

Edit: What are the ingredients listed on the bags? Very often nowadays salt and salt-based preservatives are added to frozen shrimp in order to retard water loss. It could be the case that one bag has preservatives while the other does not. This could of course affect buoyancy by changing the density of the shrimp. (In general, one should try and only buy individually quick-frozen shrimp where "shrimp" is the only ingredient.)