Betta Splendens is the name of the species, veiltail is the ame of a phenotype of tail
Betta Splendens is the type of betta (there are more than one betta!)
Veiltails is the tail type.
All VTs are splendens but not all splendens are VTs
Yeah ok, the question has already been answered a bajillion times, but I felt like saying that.
EDIT for typo