Until a better word comes to mind, I will continue to use the word respect when concerning my horses. I see the difference between horses responding out of "respect" and out of "fear". The fearful horse has not trusted the handler to be a true leader, and probably justifiably so. A respectful horse to me is attentive to it's handler as it would the leader of the herd. It is beneficial to its well being/safety. It is earned and a true partnership is formed.
When I ask my horses to do something, they know because of prior experiences with me that it is necessary. If I'm out trail riding and a situation comes up that I need the horse to look to me and trust my decision making NOW, I had better have their respect and trust. They know I will keep them safe.
Have I earned this "respect" and "trust". Yes. But , whether they are having an off day for whatever reason, too bad. But remember If I'm having an off day, well that is not allowed either, I do not get to behave poorly and badly around them either. I stay away.
This relationship is forged by our daily dealings, and each is a building block to a deeper trust. In my opinion, no infraction should be ignored because they aren't ignoring the meaning of it. Of course you deal with as little or as much attention as the situation warrants.
Someone told me once that horses are always learning. Either you be the teacher or they will be. Part of that of course is observing the "currents" in the air and taking the right course.
Respect and trust is a two way street, but only one can be the "traffic director" and that should be you.
(sorry for the ramble)