How many times do we have to drag this dead horse out in the town square and beat it again? Here's another summary again on how this works.
The App switcher in iOS displays one of the following:
Open Apps: Some iOS apps have special permissions to run in the background regardless of where you are in the OS. Examples of these apps are Pandora, Spotify and Music. They will run in the background unless you close them. An exception to this are the native Phone, Messages and E-mail apps. These apps will ALWAYS run regardless if you close them or not. Their permission is "system".
Frozen Apps: These are apps that are not actually running (cpu usage) but iOS has let them hold on to the RAM they requested just in case the user decides to use the app in the near future.
iOS will kill these apps depending on which app is the most idle and release the RAM they had reserved back into available memory pool.
Recent Apps: Not only are these apps not running (using cpu) but they are not reserving RAM either. These are just shortcuts just like Word has "recent documents". Chances are if you restart your phone and see apps listed in the taskswitcher after the restart you are staring at recent apps.
Now on to close-all debate.
Every time you close an app you force the memory it was using to be released. When you open the same app again it uses cpu cycles to re-load it into Memory.
Closing and opening apps all day uses more Battery life than it does to let them sit there in a frozen state.
Again, iOS is supposed to close idle apps on it's own and recover RAM when it needs it. As a user you do NOT need to manually do this. The ability to close an app is there just in case the app acts up, freezes or won't respond.
If I remember correctly back in the day when an App froze in iOS you could hold the home button to "force close" it but now that just triggers Siri
