Yes, they do NOT meet the shih Tzu breed size standards. Their DNA is totally Shih Tzu DNA.. Effectivly they are Shih Tzu runts.
Genetically, they are the same dog. The Chinese Imperial is the name given to those shih tzu who are under 9 pounds and under 9" tall. I have several in the 3.75 to 5 pound range and I can tell you that they are very healthy little dogs and the "myth" that they are somehow unhealthy because of their size is hogwash! There is a breed club that has been around for quite a while now dedicated to these little treasurers .. The Chinese Imperial Dog Club of America www.cidclub.com. There is also now a registry that certifies the size and pedigree's on these dogs and the registry is now registering up to 4th generation CIDs. Fourth Generation dogs have both parents registered and certified, all 4 grand parents, and all 8 great grand parents all registered and certified to be under 9 pounds and under 9" tall at at least 14 mo of age. If anyone is interested in registering their CID the website is www.Chinese-Imperial-Dog-RegistryOfAmerica.com . You can also find breeders who have certified, registered CIDs.