To me, any shoes that make sense with wool pants and a sportcoat/blazer qualifies as a "dress shoe" or "dress boot" (it may not be a "formal shoe", but that's a different concept). That means that Alden cordovan boots (especially plaza or grant last but really even barrie last), the myriad of style of E&G, G&G, Vass, etc boots, etc are all dress boots. I haven't seen a Viberg boot I would wear with wool pants and a sportcoat.
I always lumped dress and formal together. That is an interesting concept, though. My basic distinction is Oxford or Derby. Dress and casual respectively.