They are all names for the same thing. ‘Cut film’ is non-roll film, or sheet film. The shallow double sided box that holds the film can be called a film holder, a cut film holder, a double dark slide (DDS) and so on. The sliding lid that closes the box can be called the slide or the sheath. There are almost certainly more variants.
Book-form holders were the original form and they split down the middle (like a book) to drop in glass plates, but they belong to history and historical processes. If you come across one, admire the fine craftsmanship that was routine in those days.
Intrepid sell them, as do our sponsors, Morco and Nik and Trick. You may be surprised at the price. They are also available more cheaply second hand, but as always, you will have to exercise some caution. Other members may offer much better advice on second hand purchases. Chamonix make a luxury version, available from Nik and Trick.
I hope this has reduced the confusion. Photography was invented and developed by many hands so there’s some variation on nomenclature. Can you believe that there are even people who say four-by-five and eight-by-ten? Incredible, but true.