Both Uses

correspond
in
Orange Is the New Black
(Edited)

There was a system for checking out those tools: each prisoner had an assigned number and a bunch of corresponding metal chits that looked like dog tags.
p. 92.9 *

corresponding = matching
It didn't mean much in terms of getting one closer to a college degree (for that you needed to pay for correspondence courses), but it did count toward "program" credit with an inmate's case manager.
p. 157.2 *

correspondence = done from afar

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
(5) (meaning too rare to warrant focus)