Sword of Spirit
Legend
There is no correlation between HD and CR in 5e. In that sense, monsters are completely unlike 3e monsters. In 5e, CR is a hard stat, because your proficiency bonus is derived from it, rather than a soft stat that is just used for encounter building and XP as it was in 3e.
The only thing monster HD are used for is determining hit points. They are there for consistency (and in case you want to let them spend HD like PCs), but they could just as easily have assigned an arbitrary hit point value for all their effect on the creature overall. I assume they start with about the number of hit points they want a monster to have, and then give them the appropriate number of HD that, combined with their Con mod, will produce that value. There are creatures with quite low CRs and a ton of HD. I do prefer this method to arbitrary hit points, although I'm sure there are others who wouldn't care one way or the other.
The tricky part for me is "interpreting" the non-player character stats in comparison to PCs, for purposes of determining where that NPC fits in the world. (It's hard to explain what I'm getting at, but for those familiar with 3e NPC classes, that's kind of what I'm thinking of.) I finally settled with assuming their HD/hp represent about where their point of comparison to a PC should be, and the PC's greater class abilities at that HD/hp value representing the PC's elite training. It's not perfect, but I need something for my moderate simulationist approach.
The only thing monster HD are used for is determining hit points. They are there for consistency (and in case you want to let them spend HD like PCs), but they could just as easily have assigned an arbitrary hit point value for all their effect on the creature overall. I assume they start with about the number of hit points they want a monster to have, and then give them the appropriate number of HD that, combined with their Con mod, will produce that value. There are creatures with quite low CRs and a ton of HD. I do prefer this method to arbitrary hit points, although I'm sure there are others who wouldn't care one way or the other.
The tricky part for me is "interpreting" the non-player character stats in comparison to PCs, for purposes of determining where that NPC fits in the world. (It's hard to explain what I'm getting at, but for those familiar with 3e NPC classes, that's kind of what I'm thinking of.) I finally settled with assuming their HD/hp represent about where their point of comparison to a PC should be, and the PC's greater class abilities at that HD/hp value representing the PC's elite training. It's not perfect, but I need something for my moderate simulationist approach.