I generally don’t call them secure categories except when talking about it here on meta. I think I am following someone else’s example but don’t remember whose. Maybe it’s the “security” tab on the categories settings that prompted me.
Here’s how I call it in a few cases on my site.. really depends on who is involved.
Incidentally, “private messages” is also not the preferred term - I call it “personal messages” and am very up front with members that they can be (but generally are not) read by admins.
FWIW, I’ve been in this debate in my community as well - people want to create “working groups” and such, which I think is super confusing. I almost wish discourse groups had a different, special name (like flock of geese or murder of crows? rainbow of unicorns?) so the software functionality never get mixed up with the types of groupings people want to create for various purposes using the software.