What exactly is meant by this term? Does it mean that
railroads can switch each other's customers, or does it
mean that one railroad will switch an industry on behalf
of another railroad? (Difference analogous to "haulage
rights" versus "trackage rights".)

Tim, et al,

It basically means railroads switching each other's customers, with
variations on a theme.

Here's an example: In 1916 the SD&AE built it's railroad parallel to the
Santa Fe in San Diego, up from the south. Because the Santa Fe was closest
to the water (harbor), the SD&AE built to the east of it, and crossed many
spurs that the Santa Fe had going into the industrial district (now referred
to as the Gaslamp Quarter. The Santa Fe entered into a reciprocal switching
agreement whereby the SD&AE switched all the industries on the east side,
regardless of whose tracks reached them, and the Santa Fe switched all the
industries on the west side. In fact, the agreement said the SD&AE would
switch the "city side" and the Santa Fe would switch the "bay side." The
Santa Fe re-aligned its spurs to come off the SD&AE. They interchanged each
others cars, charged a fee, and settled the books monthly. The gain for
Santa Fe was the elimination of railroad crossings where the SD&AE traversed
the industrial spurs.

Another example was here in KC, where the Santa Fe, CB&Q and Wabash had
reciprocal rights for transfers, i.e., one month the Santa Fe delivered and
picked up all the transfers for the other two railroads, the next month it
was the CB&Q's turn to do all three, etc. There are plenty of other
variants.

This was all done with freight cars (required content). Hope this helps.

Keith