Is a ten speed chain, just a ten speed chain or is there a difference between SRAM and Shimano setups?

You can use either on a Shimano drive train. I'm not sure what a Shimano chain would be like on Sram though. The Shimano chain is one-directional, I'm not sure if this would mesh with the Sram teeth as well?
I prefer the Shimano ones, as I think they last longer. I carry KMC split links instead of joining pins too.