Sculpt Mode is per Object. You can have different Objects in different Modes,
First of all, make sure that you have Edit > Lock Object Modes unchecked! (Is on by default.)
Then select an Object, go into Sculpt mode. When you want to sculpt on another Object, select that one and if it is not yet in Sculpt Mode, go into Sculpt Mode for that one as well. Do that for all Objects you want to scuplt on. Now you can sculpt on the Object that is selected, as soon as you select an ohter one, you can sculpt on that one. Blender remembers the Mode of each Object.
