From Webster.com:
Purebred: bred from members of a recognized breed, strain, or kind without admixture of other blood over many generations
Recognized, meaning recognized by the CKC, AKC, UKC, etc. There are other "kennel clubs" that probably do recognize "Miniature Boston Terriers" as a purebred, but they are not the kennel clubs that reputable breeders join, but rather BYBs join in order to say that it is indeed a "papered purebred" so they can sucker people into thinking the dog comes from a great kennel and wonderful lines and make them pay an outrageous amount for essentially, a small boston terrier. So while they may seem like "purebreds" to you, to others like myself who only acknowledge breeds recognized by reputable kennel clubs like the AKC and CKC as purebreds, they are NOT purebreds, but rather undersized/smaller Boston Terriers.
This is the Boston Terrier standard, taken from the AKC site:
"Weight is divided by classes as follows: Under 15 pounds; 15 pounds and under 20 pounds; 20 pounds and not to exceed 25 pounds."
So according to the AKC (one of the larger, more recognized clubs), there are only Boston Terriers. No "Miniature Boston Terriers". A smaller boston would just be called a Boston Terrier. It's the same breed.
And honestly, if anyone was thinking about showing a dog, I would go by AKC/CKC/UKC, and not some dodgy "kennel club".