So I own the original Classic Fallout 1, 2 and Tactics games and have for a while. While looking at the store I see them, but they are named just normal Fallout 1, 2 and Tactics and the store claims I don't own them.

Is it just a difference in names or are the versions difference in some way?

Hey!

Because the question is basically the same as a previous post from not so long ago, I just post the same answer I did before.
According to one of the GOG.com Team member the games should be identical, the only difference being less bonus goodies (only the manuals, in fact) provided in the Bethesda releases and no support for OS X. You can read the original forum post here.

That's half true. It supposed to be differ and becore early of '15 it was. Now them STILL NOT IDENTICAL. Modern versions a little bit updated in bethesda launcher build and fan-made fix-mod included. Galaxy builds of Classic almost sare the same.

Offline setups suppose to remain Classic. Original Interplay UNCENSORED UNCUT content. As far as i know GOG did failed and update them sometime before linked asnwer.

So real Classic - entirely differ game in term of INGAME contents - is possible to obtain by extracting Mac Wine builds of Classic Mac setups. Inside there will be Windows build game folder.

But first doublecheck that info by installing Classic through GOG (offline) builds setups. Galaxy updated as intended. If there is no Bethesda entirely but there is Interplay mentioned in game menus, readme and else files - you are good wth what you already have. You have beset version.

another way is find pre-2014 setups but that would be difficult. and unsafe.

For Fallout 1 , you could get " Fallout Fixt " to get the uncensored version (and more fixes and addition)
For Fallout 2, there was " Fallout 2 Restoration Project " to do the same
(updated version of the restoration project : https://github.com/BGforgeNet/Fallout2_Restoration_Project )