Yes they start out as Exclusives. Occasionally they become cataloged items. This does not happen that often and always has occurred after the exclusive inventory is sold out.I was under the impression that guns supplied by LH and other distributors were exclusive and not offered by anyone else or produced outside of the limited run that distributor sold.
Has anyone bought the "exact" same gun that was sold by LH (or any other distributor) from any dealer that was not part of that limited run for a particular distributor?
This group photo has two such examples in it. It happens that they are two of my favorite 357 Magnum S&Ws

When product code 170089 was shown at SHOT in 1997 Lew Horton's intent was that only 300 of the newfangled 8 shot model 627s would be produced. I remember this vividly because I tried to get serial number 357. I was told they were not going that high and I would have to settle for some other number. So I took possession of number 27 in June, it is in the upper left corner of the picture.
In July I got a phone call asking if I still wanted number 357. The 300 pieces had sold so fast that Lew Horton decided to run 300 more, but that was going to be all they would produce. Number 357 is in the upper right of the picture. it showed up in September.
As we all know 170089 eventually became a cataloged revolver spawning off many variations over the years including the 2 5/8" 170133 UDR of 1999. That revolver has also become a cataloged firearm.

The two other variations of the UDR are also now cataloged firearms
The only long term, ongoing exclusive I can think of is the L-Comp from Camfour. That was introduced in 2000 and is still available today as an exclusive.