Commander and Chief question?

So what is the actual relationship of the Commander and Chief to a soldier. Yes he's in "charge", but he's also just a civilian. I'm just curious because people in my unit are always making Obama jokes and our leadership snap at us saying "That's your Commander and Chief!" But how is that any different than me makes a Robert Gates joke and them saying "That's your Secretary of Defense!" Their both just civilians. I mean would I have to stand at attention or salute the President?