I think about the only time you don't have to buy one of those special Classified Replacements is if you get into a family of breakers that has been absorbed by another company and absorbed again. CH BR is an example. I believe those are listed for use in Westinghouse, Bryant, Challenger, and CH BR panels. Similarly, Siemens bought out ITE, so I think those are OK. But GE and Square D Homeline seem to be unique except for Classified replacements.
There in is the question, ITE,Eaton,Westinghouse,Siemans,Homeline,,,etc,etc,.
The aquired companies and the Listed replacements, its not a simple question of who is allowed in what?
You have to research each specific one. I had a Challenger panel to deal with, and the breakers looked like Ch BR type. So I dug around on the CH web page and found a list of what older loadcenters the BR breakers can be used in. It was Bryant, Westinghouse, Challenger and perhaps a few others.
Would be nice if someone compiled a list with manufacturer documents and links (but links age out so best to have a copy of the document). Good project for an intern....
With Bryant, Challenger, Westinghouse, and CH BR series - I believe they are all the same product / product line, just the name has changed over the years, and any minor changes to designs are no different than if you look at the minor differences you will notice between say a 40 year old QO breaker and a new one. Square D has been acquired by different companies also but they choose to keep the Square D name for those lines of products, same with Cutler Hammer.