I propose plan section for a section on a horizontal plane, and sectional elevation for a section on a vertical plane.
According to Wikipedia's architectural drawing page:
A cross section, also simply called a section, represents a vertical plane cut through the object, in the same way as a floor plan is a horizontal section viewed from the top.
This would suggest that section is only appropriate for vertical planes. However, section is more generally defined as, per dictionary.com:
- a representation of an object as it would appear if cut by a plane, showing its internal structure.
Further, as a practising bridge engineer, I do not identify with the architectural definition of section only being in the vertical plane; I personally would also apply it to a cut in the horizontal plane. So I don't think it suffices for your purposes.
In my experience as a bridge engineer I often see the terms Longitudinal Section and Transverse Section. These are both sections in vertical planes. This works well for a bridge as it has longitudinal and transverse directions. Apples don't, so this doesn't really work for your situation.
An elevation is a view looking from the side. Per dictionary.com:
- Architecture. a drawing or design that represents an object or structure as being projected geometrically on a vertical plane parallel to one of its sides.
I would call a section cut, looking from the side, a sectional elevation. This may not be appropriate as it apparently has a slightly more specific definition, per Wikipedia:
A sectional elevation is a combination of a cross section, with elevations of other parts of the building seen beyond the section plane.
A plan view is looking at something from above. Wikipedia (top quote on this answer) likes floor plan for a section on a horizontal plane. Obviously an apple doesn't have a floor, but at least there seems to be some agreement on the word plan. Per dictionary.com plan means:
- Also called plan view. a drawing made to scale to represent the top view or a horizontal section of a structure or a machine, as a floor layout of a building.
In my personal experience the word plan on its own does not connotate a section, and means "without a section cut". I would therefore call a section cut, looking from above, a plan section.