Yes, all those in the chart I linked are Caridina Cantonensis. \
Caridina = Genus
Cantonensis = Species
This is the taxonomy tree for Caridina Cantonensis.
Kingdom: Animalia
Phylum: Arthropoda
Subphylum: Crustacea
Class: Malacostraca
Order: Decapoda
Infraorder: Caridea
Family: Atyidae
Genus: Caridina
Species: Cantonensis
There are other species under the Genus Caridina.
Sulawesi shrimp, for example, is a Caridina Dennerli.
Red Nose shrimp, for example, is a Caridina Gracilirostris.
A Panda / CRS would be considered different Sub-species.
Kingdom: Animalia
Phylum: Arthropoda
Subphylum: Crustacea
Class: Malacostraca
Order: Decapoda
Infraorder: Caridea
Family: Atyidae
Genus: Caridina
Species: Cantonensis
Variant: Tiger, Taiwan Bee or Crystal or whatever.
So your Variants are Taiwan Bee, Tiger, Crystal. Subspecies are usually common names.
(caveat: Taiwan Bees might not be a true Variant. We need to go further back it's line to see if Taiwan Bees are a result of Tibees. If they are then it's just another colour variant)
The difference between Crystal Red and Crystal Black would be called a "colour variation" of the same species.
Then ... Crystal Red A grade versus a SSS grade would be considered a "colour variation" of the same variant.
Your Ruby Reds, Panda, King Kongs, Wine Reds and Shadow Pandas are all colour variations of the Taiwan Bee variant.
Now this starts getting shady when we talk about hybrids.
I think Tibee (Tiger x Crystal) and Mischling (Taiwan Bee x Crystal) would be considered as a subvariant, with colour variations of it's own.
Phew. And I haven't even touched on Neocaridinas yet. But it's similar. Except Neocaridina is the Genus. Davidii is the Species.
<edit - changed the term subspecies to variant, as that is a more suitable terminology as indicated by fishmosy>