IMO, its not easy.
The CJ H&C's were distributed by 3 different distributors, CJ, Sullivan, and PS. No way to tell who unless you know the exact year issued. We know very few exact years. The issue years in our books are "best guess", at best.

We know PS sold re-issues of all 3. We know Burt made CJ's. Do we know for sure PS did not?

Personally I don't even try to define regular H&C's. The only difference I make in my files on early H&C's is CJ H&C and H&C.