I have F1, F2 and FT in my library, but they don't have the GOG preservation badge that you can see in the store (i.e, when I browse the shop, there is no "In Library" note). Are they two diffrerent games?

You probably have the old Interplay copies from before Bethesda became the owner.
After that the old store pages were removed and replaced with new ones.
The new entries consist of the same game, but miss all the extras the old entries have.