In other countries and cat registries these cats sometimes have different breed and colour names.
In England and Europe the Burmilla is a term used  only for the cat you see below in the first tile. The longhair opposite is called a Tiffanie, and the Black cat is called a Bombay -  All others are classed as "Asians" along with a colour/coat discriptor. They almost all come from the same breeding and gene pool. (Chinchilla Persian and  European Burmese)
Some few other  cats were allowed and used for a short period of time prior to year 2000. See history
New Zealand has a grouping of Silver  and Cinamon Burmese that date back to an  outcross breeding in the 70's with a domestic silver shorthair tabby. see links page "Cranreuch" They  did not get the longhair gene and chose not to differentiate the breed name.
The Australians we understand also allow outcrossing to Silver Longhair Exotic in the foundation breeding ( an "Exotic" is  a shorthair Chinchilla) and allowed repeat back breedings.See history
Canada  uses the term "Burmilla"only,  with a full colour/coat discriptor. The Chinchilla is used only once.

short hair	long hair
1 A Sable Saded silver shorthair - (Tipped)	sable shaded long hair
Champagne shaded silver sh	Champagne shaded silver  LH
Sable golden ticked  Burmilla and Sable shaded silver	a Sable golden Ticked Tabby L H
Ebony smoke (Self and wideband)	a Sable smoke Lh
a red self wideband shorthair cream  self shorthair (narrowband)	red self narrowband LH
blue self	champagne self
a blue self shorthair	long hair sable "self"
from bottom to top A Red, Havanna,  Champagne, Sable and Ebony(Bombay?)  all "selfs" and all one litter, all shorthair The deep red, deep brown (Havanna) and the Ebony are all "Full expression"	sable tortie self female LH genetically  she is  full expression chocolate - -(Havanna)
1 cameo male(red) 2 sable tortie smoke females all wide band to see the girl on the right goto	sable ,tortie, smoke (wideband) longhair
and yes this too is a Burmilla a spotted shorthair golden ticked a composite photo of one cat