I've never heard of US school photos being cut. Also photo packages from cheap studios (Sears, Target, etc.) also often come in sheets, not cut prints.
Guillotine is just one style of paper cutters (though guillotine style seems to be the most common) - I have one that has a guillotine style on one end of the board and a roller blade on the other end (roller blade cutters often offer blades for wavy or perforated cuts in addition to straight cuts). I've also seen small ones that are more or less just a small fixed blade in a sliding guide made of clear plastic (often marketed for trimming photos).