I am hesitant to reply as until recently i did not know a widget from a didgit. But since i have been looking into this i think i can safely say that most common useful widgets if added will appear in all pages.
If you need to add something into the sidebar of an individual page and it not show on other pages you can check this post which helped me.
It has to do with Custom Fields and took me some struggle to grasp and I dont want to confuse you further.
So if you dont know a custom field from a potato field you might want to keep it for future reference.
Dont worry....If this was not the answer you were looking for i am sure someone more qualified will come along........jim