One sprite sheet for one set of images, correct, it was my understanding that you wished to use images from one sprite sheet in two different scenes.
If you are using two different sets of images, then yes in most situations two different sprite sheets would be the way to go.
The image exists only once in texture memory, if you only initialize it once. OpenGL then draws that 1 single texture on the screen as many times as you'd like it to. Think of it as painting with a rubber stamp. Defining it more than once only gobbles up texture memory, it would be as useless as having several rubber stamps with the same image, you only need one, no matter how many times you are going to draw that stamp on the screen.
Spritesheets are recommend because they are a nice big fat memory palette of rubber stamps that OpenGL can use, instead of having to define each texture by itself. This speeds the process of OpenGL drawing (stamping) the textures onto the screen, as defined by you the programmer, much faster.