All 3 Uses of

correspond
in
Main Street, by Sinclair Lewis

That was her last effort to harvest the April wind, to teach divine unhappiness by a correspondence course, to buy the lilies of Avalon and the sunsets of Cockaigne in tin cans at Ole Jenson's Grocery.†
Chpt 10 *

correspondence = done from afar

Take one of these correspondence courses in drawing—they mayn't be any good in themselves, but they'll make you try to draw and——" As they reached the picnic ground she perceived that it was dark, that they had been gone for a long time.†
Chpt 30

She filed correspondence all day; then she dictated answers to letters of inquiry.†
Chpt 37 *

Definitions:

(1) (correspond as in: corresponding time period)
connect or fit together by being equivalent, proportionate, or matched

(Two things are equivalent if they have the same or very similar value, purpose, or result.)
(2) (correspond as in: corresponding by email)
communicate -- typically by writing letters or email

A corresponding secretary is an officer of an organization who is responsible for managing the organization's correspondence and keeping a record of it.
(3) (correspondence as in: a correspondence course)
done from afar

For example, a corresponding member or a correspondence course.

This sense of corresponding arose because people who lived in distant cities and could not be present for meetings, could communicate by sending written communications.
(4) (correspondent as in: foreign correspondent of the paper)
a reporter or other representative -- typically from a foreign country or with a particular expertise