Nice. I learned on a DE-9 cable making an HP-48 cable from an internal CD-ROM analog cable. I was such a poor student cliché that I used Scotch tape instead of electrical tape to ensure the RX, TX, and GND lines didn't short.

There wasn't one kind of null modem cable, per se, there were serial and parallel null modem cables.

Originally, there were null modem (serial) adapters that worked with straight through cables but that got expensive, awkward, and complicated. A universal serial null modem cable had a pair of "DB-9" DE-9 female and DB-25 female connectors on both ends so it would work with either system having either type of connector.

A parallel null modem cable had DB-25 male connectors on both ends.

http://www.nullmodem.com/LapLink.htm

Both were used with LapLink and often interchangeably called "LapLink cables" too because the boxed version of LapLink included both cables.