What do you mean with the "internal folders" are also named "sd card" seems weird to me.
Maybe you assume /sdcard is a local folder? Which it isn't that's the location of your SD card's content.
Above, when you want to access your SD card's content in your PC, it have to be dismounted from the phone which will make apps installed on it inaccessible. Mostly you have to approve the dismounting of the SD card manually from your phone. I can imagine that when AirDroid is installed on your SD card it cannot dismount it because it has some necessary files on it.