I'm sure the Biewer breeders on YT can answer this question better than me but in my opinion they are the same breed. It's a political thing related to registries.
As I understand it - One camp says that Biewers are a parti colored Yorkie from Germany & registered with a German registry, they encourage occasional breeding with standard Yorkies to help prevent the gene pool from getting too small. The other camp says Biewers are a breed made from 3 or more different breeds to be a new breed, they have another registry that they use and they only do Biewer to Biewer breedings but have a small gene pool to choose from - they are working toward AKC registration as Biewer Terriers.
Do we have any Biewer breeders who want to explain this better?
Teresa