Oh, to me an open game is knowing everything except who got which roles.
Semi-open is knowing what roles are possible, but not in what quantities.
Closed is having no idea what roles are available.
Those 3 are mutually exclusive from each other. Any of them can additionally be a role madness or bastard game.
Role madness just means there are no ordinary players. Everyone has an ability, even if it's just passive.
What you consider Bastard is personal opinion to some degree, and you can have bastard roles without it being a Bastard game. Some examples are any time the info the mod provides is false, i.e. a miller who gets a role PM saying they're ordinary town. Alignment conversions are generally a Bastard move. Role changes are a Bastard move, i.e. a doctor suddenly becomes a SK after failing to save X players. Also any roles that change the fundamental way you play, i.e. Jesters. Crab's first game didn't have any bastard elements, really. The closest was probably the dual sleepwalkers. Star Wars didn't really have Bastard mechanics either, the investigation immune Hutt my role might have been the closest things. Archer had a Framer that could be considered bastard. Cthulhu has lots of Bastard elements, to the point that it could be argued as a Bastard game. You had alignment switches, multiple teams, deaths without role reveal, hidden mechanics, RNG(I think?), and maybe more. I won't comment on Danganronpa, NX, or Election2016 while they're ongoing. Overall, we should avoid Bastard games most of the time. Cthulhu seemed to work out pretty well, but they can go bad very easily.
Note that semi-open setups can help eliminate the bastard nature of some roles. If you KNOW there's a Jester in the game, it's not nearly as annoying, for example.