Surprising... in France we learn the opposite ;) I'm a French ergonomist. I integrate the whole dimensions of work in my studies... So in the end I think we're closer than I thought ;)
Maybe it's a language thing, but I think the terms could be better defined. (the content except for the semantics of it is good though). Human factors would be more like "factors in human behavior, cognition, physical limitations that are impacted and impact a system during interaction in context of usage". Ergonomics is what you described as a study of work and tasks and users to create/design solutions to improve their work, experience, etc while taking into account the human factors. It's a scientifically based methodology(ies) to understand the users needs, with iterations and tests planned as to better target the solutions (see ISO 9241:210 for exemple). There are several specializations, physical/environmental ergonomics, cognitive ergonomics, software ergonomics, organizational ergonomics. Often a specialist will have knowledge in more than one branch. I'm not a physical ergonomics specialist, but I do have knowledge in it, while I'm a specialist in software/cognitive ergonomics and once had a contract that was oriented more towards organizational ergonomics. As reference, I have a masters in software ergonomics from an engineering school.
