Badges weren't introduced until Showtime, so there's probably not a list of 'Base Game' badges as such floating around; all of them were technically introduced with EPs. They were patched into all games that logged in, but only the achievable ones show up in game. So yeah, if your current game is just the base, that will be why a lot of badges are missing.
On my laptop, which is base + Supernatural + Island Paradise, I've only got base game-achievable plus the SN and IP released badges. The ones that I earned on my desktop game which has all EPs don't show up in the laptop game unless they're in those subsets. If you can't earn it in the game you're playing, it won't show up on the computer, although it will still show on the wall if that account has earned it.
This was originally base+IP to earn 'Who Keeps Sending These?', then I added Supernatural to earn the mauled by a bear one. Oddly, that one can't be earned with just the base game, even though the Catacombs and the Epitaph Writer job are both base game. I wonder if the specific bear mauling for the badge (there are at least five different ones) was added with SN.
