I feel that there is a pretty strong difference between GH and HR overall, though, there are always oddities.

Really, GH seems reserved for full service Hyatts that are a level above HRs -- better soap, better service, better lounges, better restaurants, better quality meeting spaces, better gyms (with better shower facilities and stocked bath supplies). Every GH I have been is a level above the HRs in the same market on these characteristics.

HRs come in three flavors --- 1. The modest full service Hyatt, usually in suburban locations, that offers a standard guest room experience and full service amenities, oriented around a practical business traveler, 2. The modest full service not-all-inclusive "resort" property (HR Lake Tahoe, HR Honolulu, some HRs in SE Asia), And 3. Large convention center hotels with 1000+ rooms. And by large, as in entire block sized floors of meeting rooms (HR Minneapolis, HR New orleans, etc). GHs (as far as I can recall) only have fairly modest meeting room space by comparison.

For Hyatt's definitions, see https://www.hyatt.com/development/ourbrands

Too add: I think of GHs much more of large-luxury-like properties. Typically they are just too large to be a true luxury property, but otherwise has great service all around that one should expect at a luxury property.