No, that spec is the failed attempt to standardize by Atwood et al., that Gruber sabotaged.
What Gruber has done is forced the spec to be called CommonMark, but as far as everyone except Gruber is concerned CommonMark is the markdown spec.
There are flavors that predate it like GFM, and extensions, but IMHO going forward it's CommonMark + possibly your extensions or it's not really Markdown.