Specific words for cross sections of different orientation

I am looking for words to differentiate between different orientations of cross sections. For example, an apple can be cut crosswise:

_{Source: Wikimedia Commons}

Or lengthwise:

_{Source: Wikimedia Commons}

What are the names for the (crosswise) cross section and the (lengthwise) cross sections?

Difference Between Longitudinal and Transverse Section

Longitudinal Section
When a vertical section is cut along the longest axis of an animal or a plant, the longitudinal cut is made. However, it is sometimes defined as the longest section cut in the vertical plane of an animal or a plant. ...
Transverse Section
Transverse section is a cut made in a plane that is made across the body of an animal, a plant, an organ, or a tissue. It is usually referred as the cut made between left and right.

(Janel Simpson)

TL;DR

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:

9. 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:

7. 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:

4. 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.