Terminology and UI for AND/OR search in Collections

I'm moving from using Tags to using Collections for my users to organize their items. (See background below for why I'm doing this.)

My issue is with AND/OR searching. For example, what would be the UI and terminology for, "Find books that are in my Horror and in my Children collections?" It's not really clear if I'm asking for just the cross section, or if I want books that are in either one of the collections. For tags, my current (radio button) options are:

  • Find things with all / any selected tags

There's then a list of selectable tags. I don't need mixes of AND and OR.

Note that these are common searches; it's not something that should be hidden away in an advanced menu. "Find books that are either thriller or mystery or dark," "Find books that are romance and Victorian"

(My site isn't about books, but same idea. Stuff to organize.)

Before you say, "Stay with tags!" see here:

A little background:

Way back when, people organized things into folders. That wasn't great because a thing can only be put into one folder. The solution to this was tags. Now a thing can have multiple tags. Books can be tagged Horror, Children, and Quick-Read. You can even use AND/OR to search tags.

That's what I use on my site. However, many people don't like tags. They ask, "how can I organize things into folders?" Tags also don't make a lot of sense when it comes to sharing. For example, people don't really think of sharing tags as in, "Here's a link to my Horror tag" or "You can see my public tags if you go to my profile."

The solution to this, it seems, is Collections. Collections are like tags (a thing can belong to many collections), but conceptionally they're more like folders: "I'm adding this book to my Horror collection" and "Here's a link to my Horror collection." I've started to see this term used more and more, for example, on Etsy, allrecipes.com, and Apple Books.