Common and standard may be synonyms under certain usages, but here, IMHO, it’s unambiguous.
Take a look at the (many) dictionary definitions of “standard.”
My take of the push back against standard is that it could imply definition 1 for standard: “official.” And I can understand Gruber not wanting an outside party to command anything official about Markdown.
Common does not have a definition that is synonymous with official. At all.
This makes sense: if I talk about “Standard English”, “Standard Practice”, or “Standard Dance”, those are very different ideas than "Common English, “Common Practice”, or “Common Dance.”
Common, used here by Jeff & co., is using common’s definition #1: “shared alike by two or more or all in question.”
It’s the Markdown parser compatibility highlight reel. It’s the subset of behaviors found most frequently across implementations. It’s the common usage.