A custom level set is the general term for a level set outside of CC1, CCLP1, CCLP2, and CCLP3, which was created with a level editor. Who made the first custom level set has not been determined, but it is variably believed to be Tyrethali Ansrath, Eric Schmidt, Dave Borgman, "Catatonic Porpoise", or even Anne Olsen.
All level packs are composed entirely of custom levels which have been subjected to a voting process to determine which levels are included and in what general order they will be placed in. On occasion, levels are modified from their original form, either simply in title or time limit, but often in the content of the level itself at the request of the level designer. CC1, of course, was the original set, and is not a custom set. Also, the CC2 levelset is not a custom levelset.
Many custom level sets can be found at David Stolp's CC website, who runs an automatic scoreboard there. Many of the expert and master-level Chipsters, including Jimmy Vermeer, Andrew Bennett, Dale Bryan, Anders Kaseorg, Evan Dummit, Mike L., John Lewis, and even David Stolp himself, have all made well-known level sets. Andrew, Evan, John, David, and Mike's sets can be found at David's site.