People are familiar with two different types of corner boxes (manual).
- In the simplest case, the workpiece is in a channel between two parallel guides, and the flat guide surfaces are perpendicular to the flat surface of the workpiece. A pair of grooves are pre-cut with parallel guides. The guide is adjusted to the desired angle along (through) their parallel surfaces.
You can insert and pass a saw through these grooves to transfer that angle to the surface of the workpiece. The corner cabinets usually I’ve seen have notches perpendicular to the horizontal material level, but I think their placement will also fit into a tricky cut.
- Another option is to hang the rear saw in the channel above the workpiece. The level of the saw blade is maintained perpendicular to the surface of the workpiece. The angle of inclination of the saw relative to the edge of the workpiece is adjustable.
In either case, the cutter body supports the saw to maintain the desired angle when cutting the workpiece. In particular, you can drive the flat part of the saw. The angle at which the teeth touch the workpiece is an indirect consequence. The teeth do not change the angle of inclination of the guide.
The miter box supports the saw blade to keep the correct angle while cutting the workpiece. On the other hand, a reciprocating saw rotates the blade for curved line cutting. This feature is achieved by using a narrow blade.
And the slot is large enough concerning the blade depth to allow the saw to be rotated. However, this property indirectly works against the miter box principle, and it can change the cutting direction.