Transverse or Cross-sections are easy to understand. A section is taken perpendicular to the long axis. This results in a circular section with most stems and roots.
Longitudinal (Long) Sections are made parallel to the long axis and result in rectangular sections.

There are two kinds of Long Sections

Radial Sections are long sections which are parallel with the Rays, and would pass through the center of the stem or root if they were large enough.

Tangential Sections are Long Sections which are perpendicular with the Rays and would never pass through the center of the stem or root.