Well, the way you described it. One could technically could consider them Cast Lanyard Series or "Lanyard Refreshers" which is what the label says.FYI, the stuff prior to 2003 aren't "Cast Lanyard Series" and they didn't come out during those years. What happened is that in 2003 when the first series proved to be successful, there was a gap between the first and second series. So they remade a bunch of old rack pins, didn't offer them for sale, but put them in the packs that were distributed to CMs to refresh their lanyard. They aren't part of a series, just something that was done to keep the lanyards looking good as well as using the lanyards to distribute pins that didn't sell out. Some were marked on Pinpics as if they were part of a series, but it was because people guessed at the time they were released, and then it wasn't cleaned up when they started doing regular yearly releases. And some of those that are listed above were cancelled Disney Store releases when Disney was in process of closing many Disney Stores the first time, prior to the sale to Children's Place, which were also distributed to lanyards instead of disposing them in another manner (there are more than what is listed above, btw). If someone were to count them because they were released on CM lanyards, then they would also want to consider the Epcot 30th pin and the couple of Conservation Station pins that were only distributed via CM lanyards.
Also, FYI, the one marked "Disneyland Cast Lanyard Series" on the Disney made checklist. The one with the Unbirthday pins, Kites, and Princesses were more commonly designated as Series 2.5 as they were released in late 2004/early 2005 between Series 2 and the "Global Lanyard Series" which later got split up into DLR and WDW Series 3.