Per the UW Burke Museum site, the correct name is C. unalaschkensis with C. canadensis listed as a synonym. I have trouble navigating the Catalogue of Life site, so thought I'd just throw it out there for clarification. I've always seen it as canadensis myself, but with all the name changes, who knows.

Catalogue of Life shows both as accepted names; two separate species. The following is from the COL website:

Cornus unalaschkensis Ledeb. - Species - accepted name
Cornus canadensis L. - Species - accepted name
Cornus canadensis var. intermedia Farr - Infraspecific taxon - synonym for Cornus unalaschkensis Ledeb.

Our database:
Bunchberry (Cornus canadensis)
Bunchberry (Cornus x unalaschkensis)

The museum is wrong. As Lin's link shows, Cornus x unalaschkensis is a hybrid taxon. It's a spontaneous hybrid of C. canadensis and C. suecica, so neither of the latter two could be a synonym.

Thanks, I at times cannot make heads or tails of taxonomy, but thought I'd bring it to the attention to those who can!