Minor Thing

Mission is too ambiguous imo...

^This.

Then what name is specific enough, but ambiguous to the point it can apply to both shadow and threatre missions, along with falsely labeled shadow missions?

Well...Shadow Missions for C3, C4 is theater until you ahve to do those other missions, which are also Shadow Missions since they take place in the Shadow Realm (save some exceptions like...assassins...), just call the rest Saga Missions or something...I don't know. I mean Technically the game treats it as Shadow Mission, and labeling it something else while not using a familiar term becomes confusing.

"Oh Saga Mission? What's that? Ohhh that Shadow Mission! Yeha I hate that stupid ruairi..."

Problem with that is things like event missions, rush of love, flashbacks like in G15, etc. They're not Saga and labeling them as Shadow is inaccurate because they're not in the shadow realm.

Non Open-World Map or Instance Based Map

Sorry, I have yet to find a shorter idea that would still be suitable/accurate.

The main problem with "mission" isn't that it's not specific enough, it's that the literal English term applies to other things like quests a lot mote than this.

How about Instanced Mission?

Perfect.