OK usand, yes, it's all opinions & perceptions In this case, I think it's our perception of the term 'respect' that is the difference. This term grates on me actually, because it's rather ambiguous & to many people seems to equate to fear and dominance. I don't think it includes either of those things.
To me, respect is something that comes out of trust and good communication, that must be earned, can't be forced. It's a 'two way street', meaning that I think respecting the horse & his way of thinking & attitudes are part of earning respect from him. It is what causes the horse to willingly and confidently do as you ask without coersion. I think trust is a necessary ingredient. You can have trust without respect, which as you point out, can make a horse rude & dangerous.
BUT I don't have a problem with clearly & fairly taught consequences to actions. Eg. I don't have a problem with punishment on occasion(prefer not to use it but won't hesitate if it seems necessary, esp for safety). It seems that this may be what you mean by respect & yes, I agree that I wouldn't work on trust at the expense of ignoring that, but likewise I don't do this exclusively either, but in a clear & consistent way, without anger, to encourage them to trust me. You can have obedience and submissiveness without respect.