Another format difference besides newlines: CommonMark allows footnotes/link-definitions within a blockquote. Example in %ithrMtt....

More complete differences between GFM and CommonMark (and Original), according to remark-parse:

GFM mode (boolean, default: true) turns on:

• Fenced code blocks
• Autolinking of URLs
• Deletions (strikethrough)
• Task lists
• Tables

CommonMark mode (boolean, default: false) allows:

• Empty lines to split blockquotes
• Parentheses (( and )) around for link and image titles
• Any escaped ASCII-punctuation character
• Closing parenthesis ()) as an ordered list marker
• URL definitions (and footnotes, when enabled) in blockquotes

CommonMark mode disallows:

• Code directly following a paragraph
• ATX-headings (# Hash headings) without spacing after opening hashes
  or and before closing hashes
• Setext headings (Underline headings\n---) when following a paragraph
• Newlines in link and image titles
• White space in link and image URLs in auto-links (links in brackets,
  < and >)
• Lazy blockquote continuation, lines not preceded by a closing angle
  bracket (>), for lists, code, and thematicBreak